Supply and Demand

  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?
  2. x = __ months
  3. 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.
  4. I = $_________
  5. 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.
    Total cost = 5x + 4480 and Total revenue = 15x
    How many thumb drives must Burnem sell to break even?
  6. x = _ thumb drives
  7. 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
  8. What is the projected population in 2022? y= _
  9. In what year is the population predicted to be 67.2 million? _
  10. 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.
  11. What t-value corresponds to 2025? t= _
  12. Find the predicted U.S. per capita real disposable income (to the nearest $10)
    in 2025. $_____________
  13. In what year is the U.S. per capita real disposable income expected to exceed
    $55,000? _
  14. A linear revenue function is R = 38x. (Assume R is measured in dollars.)
  15. What is the slope m? m = _
  16. What is the marginal revenue MR ? MR =__
  17. What is the revenue received from selling one more item if 50 are currently being
    sold? __
  18. What is the revenue received from selling one more item if 100 are being sold?

  1. A linear revenue function is R = 38.69x.
  2. What is the slope m? m =__
  3. What is the marginal revenue MR? MR =_
  4. What is the revenue received from selling one more item if 46 are currently being
    sold? __
  5. What is the revenue received from selling one more item if 81 are being sold?

  1. Let C(x) = 3x + 650 and R(x) = 28x.
  2. Write the profit function P(x). P(x) = __
  3. What is the slope m of the profit function? m =__
  4. What is the marginal profit MP ? MP = __
  5. 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.)
  6. For this helmet, write the function for monthly total costs C(x).
    C(x) = _
  7. Write the function for total revenue R(x).
    R(x) = __
  8. Write the function for profit P(x).
    P(x) = __
  9. Find C(200).
    C(200) = __
  10. Find R(200).
    R(200) = _
  11. Find P(200).
    P(200) = __
  12. Find C(300).
  13. C(300) = __
  14. Find R(300).
    R(300) = __
  15. Find P(300).
    R(300) = __
  16. Find the marginal profit MP. MP = _