Ask Question
10 December, 23:32

The value of Sara's new car decreases at a rate of 8% each year. Write an exponential function to model the decrease in the car's value each month.

+1
Answers (1)
  1. 10 December, 23:43
    0
    Example: Value = 20,000 (2.98/3) ⁿ

    Explanation:

    The function of a decay exponential function with decreasing rate r is:

    y = A (1 - r) ⁿ

    For example: y = 10 (1 - 0.1) ⁿ, is a exponential function with decreasing rate 0.1 or 10%.

    Then, for the given decreasing rate of 8% yearly, we fiirst find the monthly rate by dividing by 12: r = 8% / 12 = 0.08 / 12 = 0.02 / 3.

    With that, the general form of the searched function to model the decrease in the car's value eah month is:

    Value = A (1 - 0.02/3) ⁿ = A (2.98 / 3) ⁿ

    In that equation, A is the initial value of the car.

    Suppose a car whose initial value is $ 20,000, then the function (model) is:

    Value = 20,000 (2.98/3) ⁿ

    You van verify the validity of that model by doing a table:

    Month value 20,000 (2.98/3) ⁿ

    0 20,000 (2.98 / 3) ⁰ = 20,000

    1 20,0000 (2.98 / 3) = 19,866.67

    3 20,000 (2.98 / 3) ² = 19,734.22

    4 20,000 (2.98 / 3) ³ = 19,602.66

    And now calculate the rate of decrease of the value for any consecutive pair of months.

    For example for months 3 and 4, rate of decrease = [19,734.22 - 19,602.66] / 19,734.22 = 0.006667 monthly.

    Multiply by 12 to find the rate per year: 0.006667 (12) = 0.08 = 8%
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “The value of Sara's new car decreases at a rate of 8% each year. Write an exponential function to model the decrease in the car's value ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers