Ask Question
12 July, 01:17

A car that originally cost $20,000 depreciates (loses value) by 15% each year. In about how many years will the car be worth half its value? Use the equation 10,000 = 20,000 (0.85) ^x to solve the problem. Round your answer to the nearest dollar.

? years

+1
Answers (1)
  1. 12 July, 03:28
    0
    Is the question - did they mistakenly say "dollar" rather than "years?"

    x = # of years

    10,000 = 20,000 (0.85) ^x, first divide both sides by 20,000

    0.5 = (0.85) ^x, next take the ln of both sides

    ln 0.5 = ln (0.85) ^x, by rules of logarithms you may move x to make it a coefficient of the logarithm

    ln 0.5 = x (ln 0.85), divide both sides by ln (0.85)

    x = (ln 0.5) / (ln 0.85) = (-0.693) / (-0.1625) = 4.26 years
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A car that originally cost $20,000 depreciates (loses value) by 15% each year. In about how many years will the car be worth half its ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers