Posted: February 26th, 2022

Math

1. A $642,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by y = 642,000 − 1800x dollars. After how many months will the value of the building be $393,600?

1. x = ________ months

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2. High interest rates make it difficult for people to pay off credit card debt in a reasonable period of time. The interest I (in dollars) paid on a $10,000 debt over 3 years when the interest rate is r% can be approximated by the equation shown below.

I/175.393 + 0.663 =r If the credit card interest rate is 15.8%, find the amount of interest paid during the 3 years.

1. I = $_________

3. Burnem Inc. manufactures thumb drives and sells them to a distributor. Burnem's total cost and total revenue (in dollars) for x thumb drives are given by the following equations.

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Total cost = 5x + 4480 and Total revenue = 15x How many thumb drives must Burnem sell to break even?

1. x = ___________ thumb drives

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4. Using data from 2010 and projected to 2020, the population of the United Kingdom (y, in millions) can be approximated by the equation

10.0y − 4.55x = 581 1. What is the projected population in 2022? y= ___________ 2. In what year is the population predicted to be 67.2 million? _____________

5. Disposable income, the amount left after taxes have been paid, is one measure of the health of the economy. Using U.S. Energy Information Administration data for selected years from 2015 and projected to 2040, the U.S. real disposable income per capita (in dollars) can be approximated by the equation

I = 707.6t + 39,090 where t is the number of years after 2015.

1. What t-value corresponds to 2025? t= _________ 2. Find the predicted U.S. per capita real disposable income (to the nearest $10)

in 2025. $_____________ 3. In what year is the U.S. per capita real disposable income expected to exceed

$55,000? ___________ 6. A linear revenue function is R = 38x. (Assume R is measured in dollars.)

1. What is the slope m? m = _______ 2. What is the marginal revenue MR ? MR =______

3. What is the revenue received from selling one more item if 50 are currently being sold? ______________

4. What is the revenue received from selling one more item if 100 are being sold? _________________

7. A linear revenue function is R = 38.69x. 1. What is the slope m? m =__________ 2. What is the marginal revenue MR? MR =_______ 3. What is the revenue received from selling one more item if 46 are currently being

sold? ____________ 4. What is the revenue received from selling one more item if 81 are being sold?

_______________

8. Let C(x) = 3x + 650 and R(x) = 28x. 1. Write the profit function P(x). P(x) = ____________ 2. What is the slope m of the profit function? m =__________ 3. What is the marginal profit MP ? MP = __________

9. Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $5500 per month. Materials and labor for each helmet of this model are $20, and the company sells this helmet to dealers for $40 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.)

1. For this helmet, write the function for monthly total costs C(x). C(x) = ___________

2. Write the function for total revenue R(x). R(x) = ____________

3. Write the function for profit P(x). P(x) = ____________

4. Find C(200). C(200) = ____________

5. Find R(200). R(200) = ___________

6. Find P(200). P(200) = ____________

7. Find C(300). 8. C(300) = __________ 9. Find R(300).

R(300) = __________ 10. Find P(300).

R(300) = __________ 11. Find the marginal profit MP. MP = ________

10. A jewelry maker incurs costs for a necklace according to C(x) = 39x + 1650.

If the revenue function for the necklaces is R(x) = 69x

How many necklaces must be sold to break even? ___________ necklaces

11. A manufacturer sells belts for $15 per unit. The fixed costs are $2500 per month, and the variable cost per unit is $10.

Write the equations of the revenue R(x) and cost C(x) functions.

R(x) = _______________

C(x) = _______________

Find the break-even point. It takes _______ units to break even.

12. Electronic equipment manufacturer Dynamo Electric, Inc. makes several types of surge protectors. Their base model surge protector has monthly fixed costs of $1275. This particular model wholesales for $11 each and costs $3.50 per unit to manufacture. Write the function for Dynamo's monthly total costs.

C(x) =___________

Write the function for Dynamo's monthly total revenue.

R(x) = _____________

Write the function for Dynamo's monthly profit.

P(x) = ______________

Find the number of this type of surge protector that Dynamo must produce and sell each month to break even.

___________ surge protectors

1. The owner of a $642,000 property uses the straight-line depreciation technique to depreciate it for tax purposes. The building's value, y, after x months of use is given by y = 642,000 1800x dollars. In how many months will the building's value be $393,600?

1. x months = months

2. People find it difficult to pay off credit card debt in a fair amount of time due to high interest rates. The equation below can approximate the interest I (in dollars) paid on a $10,000 debt over three years when the interest rate is r percent.

r = I/175.393 + 0.663 Determine the amount of interest paid over the course of three years if the credit card interest rate is 15.8 percent.

1. I am $

3. Brunem