Suppose x grows at a constant rate g x
=5 percent per year. Similarly, suppose y grows at a constant rate g y
=1 percent per year. Suppose the value for x t
at time t=0 is equal to 3 (that is, x 0
=3 ), and that the value for y t
at time t=0 is equal to 2 (that is, y 0
=2 ). Finally, suppose z t
=x t
0.5
y t
0.5
. (a) Calculate the numerical value for z 0
(that is, z t
at time t=0 ). Show every step of all calculations. (b) Derive the expression for the growth rate of z t
(denoted by g z
) as a function of g x
and g y
. Show every step of all calculations. (c) Derive the expression for z t
as a function of g x
,g y
,z 0
, and t. Show every step of all calculations. (d) Calculate the numerical for z 5
and z 10
(that is, z t
at time t=5 and at time t=10 ) by using the expression that you derived in part (c). Show every step of all calculations.
Answers
The numerical values of z(5) and z(10) are approximately equal to 2.16266 and 2.71586, respectively.
a) Calculating the numerical value for z0
We know the value of x0 and y0 and the formula for z0 is given as:
z_0 = x_0^{0.5} y_0^{0.5}
Since x0=3 and y0=2,
substituting these values into the formula for z0 we get:
z_0 = x_0^{0.5} y_0^{0.5}=3^{0.5} \2^{0.5} = 1.73205
Thus, the value of z0 is approximately equal to 1.73205.
b) Deriving the expression for the growth rate of z(t)
We know that z(t) = x(t)^0.5 y(t)^0.5.Using the chain rule of differentiation and the given growth rates of x and y, we can obtain the expression for the growth rate of z(t):
g_z(t) = {d}{dt}t[{x(t)} {y(t)}\right]
g_z(t) = {1}{2} ({1}{{x(t)}}{dx(t)}{dt}) {y(t)} + {1}{2} {1}{{y(t)}} {dy(t)}{dt}{x(t)}g_z(t) = {1}{2} {g_x(t)}{2{x(t)}} {y(t)}{1}{2} {g_y(t)}{2{y(t)}} {x(t)}\right)
g_z(t) = \{1}{4} g_x(t) {{y(t)}{x(t)}} + {1}{4} g_y(t){x(t)}{y(t)}}
Therefore, the expression for the growth rate of z(t) as a function of g_x and g_y is:
g_z(t) = {1}{4} g_x(t){y(t)}{x(t)}} +{1}{4} g_y(t) {x(t)}{y(t)}}
c) Deriving the expression for z(t)We are given that z(t) = x(t)^0.5 y(t)^0.5.
Using the given growth rates for x and y, we can obtain the expression for x(t) and y(t):
g_x = 0.05
x(t) = x_0 e^{g_x t}
x(t) = 3 e^{0.05 t}
g_y = 0.01
y(t) = y_0 e^{g_y t}
y(t) = 2 e^{0.01 t}
Substituting these expressions for x(t) and y(t) into the expression for z(t), we get:
z(t) = x(t)^{0.5} y(t)^{0.5
z(t) = (3 e^{0.05 t})^{0.5} (2 e^{0.01 t})^{0.5}
z(t) = \sqrt{3} \sqrt{2} e^{0.03 t}
z(t) = 1.73205 e^{0.03 t}
Therefore, the expression for z(t) as a function of g_x, g_y, z0, and t is:
z(t) = z_0 e^{(g_x+g_y)/2 t}
z(t) = 1.73205 e^{0.03 t}
d) Calculating the numerical value of z(5) and z(10)Using the expression for z(t) that we derived in part (c), we can calculate the numerical value of z(5) and z(10) as follows:
z(5) = 1.73205 e^{0.03 \cdot 5}
z(5) = 2.16266
z(10) = 1.73205 e^{0.03 \cdot 10}
z(10) = 2.71586
Therefore, the numerical values of z(5) and z(10) are approximately equal to 2.16266 and 2.71586, respectively.
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Related Questions
Business-to-business marketing involves the marketing of goods and services to organizations for use in the creation of goods and services that ______.
Answers
The marketing of goods and services to organizations so that they could create more goods and services that add value is known as business-to-business (B2B) marketing.
What is Business-to-Business?Business-to-business means the business relationship between an entity and another. The organizations that buy B2B goods and services use them for either:
ResaleProduction Support of their works.Thus, business-to-business marketing involves the marketing of goods and services by one organization to other organizations for use in the creation of goods and services that add value.
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What does purchasing insurance for a business reveal about the owner's attitude toward financial risk?
1. It shows that the owner expects financial risk and is eliminating it by making an insurance company liable.
2. It shows that the owner acknowledges the financial risks and is willing to pay every month to transfer the risk to an insurance company.
3. It shows that the owner is willing to share ownership of the business to reduce financial risk.
4. It shows that the owner is willing to budget for short-term financial risks to avoid long-term risks.
Answers
Purchasing insurance for a business mainly reveals that "the owner acknowledges the financial risks and is willing to pay every month to transfer the risk to an insurance company."
What is the purpose of insurance?The purpose of insurance is to have coverage or a backup in case of unexpected negative events. For example, with health insurance companies or people pay a small amount of money every month to make sure expenses are at least partially covered if there is a medical emergency occurs.
Why do some business owners pay for insurance?Similarly, business owners paying for insurance expect to have some financial support in case a negative event occurs regarding the business. This shows they are aware of risks and want to transfer this or decrease it by paying.
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The most productive way to find a job lead is to
a. find advertisements on the Internet
b. network
c. find advertisements in the newspaper
d. read brochures from professional organizations
Please select the best answer from the choices provided
A
В
C
D
Answers
Answer:
B. Network
Explanation:
took quiz on edge
Answer:
B
Explanation:
Another name for a substandard risk classification is
A. Elevated
B. Rated
C. Controlled
D. Decline
Answers
The right response is B. Rated. A different term for a substandard risk categorization.
Two further names for inferior risk categories are impair risk and life insurance with a table rating. People with significant health problems are categorised as posing a low risk. Depending on their risks, these individuals can be compelled to pay an extra cost or a "table rating" to the issuing life insurance company. The three risk groups that insurance companies employ the most commonly are super preferred, preferred, and standard. The specific qualifications might differ from company to company, even though the standards for each class don't. If applicants don't meet the prerequisites for these classes, they risk being classified as substandard.
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Write a short paragraph describing the benefits of working as a team to complete a project.
Answers
Answer:
A group of people who have to achieve common goal is known as team. If we work in team it increases our creativity and learning, it also builds trust. It boost the particular person when we work in team. We can also learn faster. There are more chances of getting success in particular area if we work in team. As there is saying, " together we can achieve more what each of us can achieve." It also enhances productivity and capability.
Brownsville Novelty Store prepared the following budget information for the month of May: Sales are budgeted at $360,000. All sales are on account and a provision for bad debts is made for each month at three percent of sales for the month. Inventory was $84,000 on April 30; an inventory increase of $12,000 is planned for May 31. All inventory is marked to sell at cost plus 50 percent. Estimated cash disbursements for selling and administrative expenses for the month are $48,000. Depreciation for May is projected at $6,000. Brownsville's budgeted bad debts expense for May is:
Answers
Answer: $10800
Explanation:
Brownsville's budgeted bad debts expense for May will be calculated by multiplying the sales budgeted for May by the percentage allocated to the provision for bad debt. This will be:
= $360,000 × 3%
= $360,000 × 3/100
= $360,000 × 0.03
= $10800
Brownsville's budgeted bad debts expense for May is $10800
Zion company sells merchandise on credit to brc, inc. in the amount of $1,200. the entry to record this sale would include a: (check all that apply.)
Answers
The entry to record the sale of merchandise would include
-Debit to Accounts Receivable
-Credit to Sales
What is journal entry?Journal entry refers to how business transactions are recorded for ease of reconciliation.
Typically, when goods are sold, the accounts receivable is debited, while sales is credited.
Hence, the entry to record the sale of merchandise would include debit to Accounts Receivable and credit to sales.
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A
person who
owns stock in a
corporation.
Answers
Frank borrowed $25,000 for a period of 4 years. His interest rate is 3%. How much interest will Frank pay in all?
Answers
Frank will pay the total amount of $28,000 with an interest of $3000.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.
We have been given data as:
Principal (P) = $25,000
Rate of Interest (R) = 3%
Time (T) = 4 years
⇒ Simple interest = P × R × T
Substitute the value of P, R, and T in the above formula,
⇒ Simple interest = 25,000 × 3% × 4
⇒ Simple interest = 25,000 × 3/100 × 4
⇒ Simple interest = 25,000 × 0.03 × 4
Apply the multiplication operation, and we get
⇒ Simple interest = $3000
Total payback amount = $25,000 + $3000 = $28,000
Therefore, he will pay the total amount of $28,000 with an interest of $3000.
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List five steps of the budget process
Answers
Answer:
1)The President submits a budget request to Congress
2)The House and Senate pass budget resolutions
3)House and Senate Appropriations subcommittees "markup" appropriations bills
4)The House and Senate vote on appropriations bills and reconcile differences
5)The President signs each appropriations bill and the budget becomes law
Explanation:
I put the five federal budget process steps. Hope this helps :)
The government has many obligations to provide services to its tax-paying citizens. If you were in Congress, how
would you balance the need for the government to spend money on necessary things with a prudent approach to controlling the debt and the deficit? Use examples in your answer.
Answers
A government is considered to have a budget surplus if it raises more revenue through taxes than it spends. A budget that is balanced means that taxes and spending are equal. The government debt is the total of all prior surpluses and deficits.
What is Budget surplus?A budget surplus occurs when income exceeds expenses. The term is commonly used to describe a government's financial status since citizens have "savings" instead of a "budget surplus." A surplus is evidence of a government's capacity to manage its finances appropriately.
Example,
A resource or good is said to have a surplus if there is more than is presently being utilized. A surplus can refer to a variety of items, such as cash, goods, assets, and earnings. A surplus in the sense of inventory refers to items that remain on store shelves but have not yet been purchased.
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When filing for funds from the illinois real estate recovery fund, complainants must provide court documents, relevant transaction documents, and ______.
Answers
Complainants are required to submit court documents, pertinent transaction documentation, and an itemized account of alleged damages when requesting money from the Illinois real estate recovery fund. The claimant must swear under oath that damages are estimated and that the assessment is as precise as the circumstances allow if an itemized statement is not available.
What are funds ?A fund is a group of funds put aside for a specific purpose. A fund may be established to fulfill a number of goals, including the development of a new civic center by the local government, the giving of educational scholarships, or the settlement of customer claims by an insurance company.
People, businesses, and governments use funds to save money. People may establish an emergency fund, also known as a rainy-day fund, or a trust fund to save money for a specific person in order to handle unforeseen expenses.
Individual and institutional investors can put money into a variety of funds with the goal of making money. Examples include mutual funds, which pool money from different investors and invest it in a wide portfolio of assets, and hedge funds, which invest the assets of high-net-worth individuals (HNWI) and institutions in a way that is meant to create returns above the market. Governments use funds, such as special revenue funds, to pay for specific public expenses.
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For what purpose are goods and service produced in a socialist economy
Answers
Answer: The options are missing from the question,the options are;
A) Profits
B) Their usefulness
C) To create demands
D) To meet all consumer needs.
The correct answer to the question is option D
In a capitalist economy,goods and services are being produced for the sole aim of making profits and to accumulate capital, but when we talk about the SOCIALIST ECONOMY,it differs from the capitalist economy and the sole aim is different.
Socialist economy employs a technique known as usage value in the meeting of the needs and wants of the people, this prevents the over production or under production of goods and services based on their rewards and usage.
In socialist economy,goods are services are produced and those goods and services are made directly accessible to the people that is the masses. A scarce economic resources in a socialist economy are being utilized judiciously inorder to meet the needs of the consumers and make them satisfied in every way possible.
10)
How might a mission statement help Donna with her new
business?
Answers
A mission statement can help Donna with her new business by providing clarity and direction for her venture. It serves as a guiding statement that outlines the purpose, values, and goals of the business.
It helps Donna align her decisions, actions, and strategies with the overall mission, facilitating focus and consistency in her business operations. A mission statement is a concise statement that articulates the purpose and core values of a business. It outlines what the business aims to achieve and how it intends to operate. For Donna, having a mission statement for her new business can provide several benefits.
Firstly, it helps Donna define the purpose and direction of her business. It clarifies the reason for starting the business and what it aims to accomplish, providing a sense of focus and clarity.
Secondly, a mission statement helps Donna communicate her business's values and principles to stakeholders, including employees, customers, and investors. It sets the foundation for building a strong company culture and aligning everyone's efforts toward a common goal.
Lastly, a mission statement can serve as a guide for decision-making and strategy development. When faced with choices or challenges, Donna can refer to her mission statement to ensure that her actions align with the overall purpose and values of her business.
A mission statement plays a crucial role in helping Donna with her new business by providing clarity, guiding decision-making, and aligning stakeholders toward a common vision.
In conclusion, a mission statement can significantly benefit Donna in her new business. It provides clarity and direction, communicates values to stakeholders, and guides decision-making and strategy development. By establishing a mission statement, Donna can effectively define her business's purpose and goals, foster a strong company culture, and make informed decisions that align with her business's overall mission. This helps create a solid foundation for success and growth in her new venture.
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When making decisions, managers often must decide between doing what is beneficial for the firm in the short term, and what is beneficial for both the firm and society in the long term. To address this conflict, a firm must
Answers
When making decisions, managers are often faced with a conflict between what is beneficial for the firm in the short-term and what is beneficial for both the firm and society in the long-term.
This conflict arises because the actions that benefit the firm in the short-term may not necessarily align with the interests of society as a whole, which can lead to negative consequences for both the company and society in the long-term.
To address this conflict, a firm must adopt a long-term orientation and consider the broader social and environmental impacts of its decisions. This means looking beyond immediate financial gains and recognizing that actions taken today can have far-reaching implications for the company's reputation, customer loyalty, employee morale, and overall sustainability.
Firms that prioritize social responsibility and sustainable business practices are more likely to build strong relationships with stakeholders, including customers, employees, investors, and regulators. They are also better equipped to weather economic downturns and other disruptions, as they have diversified their risk and invested in building resilient supply chains and communities.
Ultimately, the key to addressing the conflict between short-term gains and long-term benefits is a commitment to corporate social responsibility (CSR) and sustainable business practices. By prioritizing the needs of society and the environment alongside those of shareholders, firms can create value for all stakeholders over the long-term, ensuring their continued success and impact.
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Unpredictable policies can result in conflict because employees may ______.
a.
Believe that there is a double standard
b.
Have to guess at what the policies actually are
c.
Give out information that is incorrect
d.
All of the above
Answers
Answer:
All of the above
Explanation:
D.
Answer:
D
Explanation:
Above
homework libABC Inc. uses a machine that can produce 95 cranks per hour. The firm operates 9 hours per day, six days per week. Due to regularly scheduled preventive maintenance, the firm expects the machine to be running during approximately 90% of the available time. Based on experience with other products, the firm expects to achieve an efficiency level for the cranks of 80%. What is the expected weekly output of cranks for this company
Answers
The expected weekly cranks output should be 3,693.60.
The following formula should be applied:
= Number of cranks produced per hour × number of hours operated per day × number of days per week × expected machine running percentage × efficiency level
= 95 × 9 × 6 × 90% × 80%
= 3,693.60
Therefore we can conclude that The expected weekly cranks output should be 3,693.60.
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fasb standards affect the department of a company.multiple choiceadvertisinghuman resourcemarketingcustomer serviceaccounting
Answers
FASB standards primarily affect the E. Accounting department of a company.
The FASB (Financial Accounting Standards Board) is a private, non-profit organization that sets accounting standards for public companies and other organizations in the United States. The FASB standards provide guidance on how companies should report their financial transactions and events in their financial statements, such as income statements, balance sheets, and cash flow statements.
The accounting department of a company is responsible for recording financial transactions and preparing financial statements. The department must follow the FASB standards when preparing financial statements to ensure they are accurate and reliable. FASB standards cover a wide range of topics, including revenue recognition, inventory accounting, lease accounting, and financial statement presentation.
Other departments of a company, such as advertising, human resources, marketing, and customer service, are not directly affected by FASB standards. However, these departments may indirectly be affected by accounting policies and practices established by the accounting department. For example, the accounting department may establish policies on how to account for advertising expenses, which may impact the advertising department's budget.
Similarly, the accounting department may establish policies on how to account for employee benefits, which may impact the human resources department's policies on employee compensation and benefits. Therefore, the correct option is E.
The question was incomplete, Find the full content below:
FASB standards affect the department of a company.multiple choice
A. advertising
B. human resource
C. marketing
D. customer service
E. accounting
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Benefits Offered "Must-Haves":
Answers
Under a contractionary taxation policy, the government can reduce the deficit by
A) increasing taxes.
B) reducing taxes.
C) increasing spending.
D) increasing inflation.
The Answer is A) increasing taxes.
Answers
Answer:
c
Explanation:
not sure but I tried may best tho
Answer:
A) increasing taxes.
Explanation:
What is the best way to use a credit card to build your credit history?
Answers
Answer:
All you have to do is pay off your credit card bill in full and on time each month, and just keep doing that.
Explanation:
If the resources that an entrepreneur uses have a higher value if used for other production, the entrepreneur will
Answers
Answer:c
Explanation:
An entrepreneur should focus his or her efforts on ventures that will provide the most profit.
If they invested in something else, they would lose money since the project they chose would yield less profit than the optimal one that would have yielded more.
Thus, Lose Money is correct.
What is the most important resource for business owners?Human capital, sometimes known as "talent" or "employees," was frequently the most highly regarded resource among those polled.
Management and technical workers were regularly mentioned as being very significant by respondents. Debt and equity capital are used to provide access to funding or finance.
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13. Olive Baker has a paycheck for $173,45 and a refund check for $3. She
would like to receive $25 in cash and deposit the remaining amount.
What is her total deposit?
Answers
Answer:
$151.45
Explanation:
Olive had two checks; the total for the two checks is
=$173,45 + $3
=$176.45
Olive wishes to have $25 in cash, net deposits
= $176.45 - $25
=$151.45
The management of Paul's Planes, Pugs and Plushes inc., believes that when managers pursue their activities in the right way, positive outcomes will result. This approach is described as management by ________ . a. objectives b. goal c. indicator d. outcome e. means
Answers
The approach employed by the management in pursuing their activities in the right way is known as means approach.
What is a means approach?A means approach refers to a business approach which is based on the theory that if they pursue their activities in the right way, then, a positive outcomes will result.
Hence, the approach employed by the management is known as means approach.
Therefore, the Option E is correct.
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What is an audiologist?
Answers
Answer:
An audiologist is a licensed healthcare professional who specializes in diagnosing and treating hearing
Explanation:
Answer:
Audiologists are health care professionals who identify, assess and manage disorders of hearing, balance and other neural systems.
Explanation:
An audiologist is a licensed hearing health care professional who specializes in the diagnosis and treatment of hearing loss and balance disorders in adults and children. ... Treatment for balance disorders and tinnitus (ringing in the ears) Hearing and speech rehabilitation programs.
Also:
An audiologist is a licensed healthcare professional who specializes in diagnosing and treating hearing, balance and tinnitus disorders and who has, at minimum, a master's degree. Many, however, also go on to get a doctorate degree (Au. D.), and only then become a Doctor of Audiology.
state any 5 tpyes of legal requirements that will be required to a business
Answers
Diego feels he has achieved some measure of respect as a cosmetic surgeon. Now, Diego focuses on being the best he can be. Which need is Diego trying to meet
Answers
Diego is trying to focus and meet his self-actualization needs.
What is Maslow's Hierarchy of Needs?
Abraham Maslow's theory of Hierarchical needs explains that people are driven to meet fundamental wants before moving on to more complex requirements.
His theory emphasizes five hierarchical needs, these are:
Physiological needsSecurity and safety needsSocial NeedsEsteem NeedsSelf Actualization needsTherefore, based on the fact that Diego is concerned about his own personal growth and focusing on his career, we can conclude that Diego is trying to focus and meet his self-actualization needs.
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How important is money
Answers
Answer:
very important
Explanation:
money is a global income source for everyone. we all have different types but it is all still money. now say one country got rid of money and had people pay for stuff using other things. if china did that lots of different countries wouldn't be able to get stuff from there unless they had so much of that product they could just give it up.
a corporation intends to raise additional funds from its existing shareholders to avoid diluting their interest in the company. the corporation will be engaging in a:
Answers
Offering of rights. The business will participate in a rights offering. All of its current common stockholders receive the rights, which entitle them to buy a pro rata share of the new stock.
Briefing:-They can keep owning the same percentage of the company's equity if they subscribe for the extra shares. The subscription price is set below the stock's current market value. If the offering is a success, the issuer can close the offering without an underwriter and save a lot of money in the process. Shares are sold in primary and secondary offers to new shareholders, not to current shareholders.
Why is preferred stock convertible?A type of preferred share known as convertible preferred stock pays a dividend and, after a set period of time, can be converted into common stock at a fixed conversion ratio.
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The following graph shows the daily market for jeans. Suppose the government institutes a tax of $11.60 per pair. This places a wedge between the price buyers pay and the price sellers receive.
Answers
The graph demonstrates that the quantity is fifty, and the price is one hundred dollars before tax. Giving share of the tax burden as= $5.60
How does the graph demonstrate the cost of the item?In the context of the whole inquiry, it is possible to deduce from the graph that the quantity is fifty and that the price, excluding tax, is one hundred dollars.
In addition, the quantity is 45, and the price after tax is $105.60, each in its own right. As a result of the rise in the tax rate, there was a subsequent decrease in the amount that was requested.
And finally, the following will constitute the purchasers' share of the tax burden:
= $105.60 - $100
= $5.60
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