Question

A construction company paid $85,000 for a new fork lift. The fork lift depreciates at a rate of 15% per year. How long will it take until the value of the fork lift is below $10,000?

Answer 1

13.2 years

Explanation:

The decay rate is 15%, so the decay factor is 1 - 15% = 0.85. Then the exponential equation for the value is ...

v(t) = 85000·0.85^t

We can set v(t) = 10,000 and solve for t:

10000 = 85000·0.85^t

10000/85000 = 0.85^t . . . . divide by 85000

log(2/17) = t·log(0.85) . . . . . .reduce fraction, take logs

t = log(2/17)/log(0.85) ≈ 13.2

It will take about 13.2 years for the value to fall below $10,000.

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Such a question is nicely answered by a graphing calculator.