Ask Question
2 July, 06:42

A car with an initial cost of $23,000 is decreasing in value at a rate of 8% each year. Write the exponential decay function described in this situation. Then use your function to determine when the value of the car will be $15,000, to the nearest year.

+4
Answers (1)
  1. 2 July, 07:19
    0
    Step-by-step explanation:

    We would apply the formula for exponential decay which is expressed as

    A = P (1 - r/n) ^ nt

    Where

    A represents the value after t years.

    n represents the period for which the decrease in value is calculated

    t represents the number of years.

    P represents the value population.

    r represents rate of decrease.

    From the information given,

    P = 23000

    r = 8% = 8/100 = 0.08

    n = 1

    Therefore, the exponential decay function described in this situation is

    A = 23000 (1 - 0.08/n) 1) ^ 1 * t

    A = 23000 (0.92) ^t

    If A = 15000, then

    15000 = 23000 (0.92) ^t

    0.92^t = 15000/23000 = 0.6522

    Taking log of both sides to base 10

    Log 0.92^t = log 0.6522

    tlog 0.92 = log 0.6522

    - 0.036t = - 0.1856

    t = - 0.1856 / - 0.036

    t = 5 years to the nearest year
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “A car with an initial cost of $23,000 is decreasing in value at a rate of 8% each year. Write the exponential decay function described in ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers