Answer:
8.5 years
Explanation:
You want to know the number of years until 18500 depreciates to 9100 at the rate of 8% per year.
Value
The depreciation rate given as a percentage of current value tells you the depreciation is exponential. The formula will be ...
value = (initial value) × (1 - (depreciation rate))^t
where the rate is "per year" and t is in years.
Application
value = 18500·(1 -0.08)^t
9100 = 18500·0.92^t . . . . fill in the value of interest
9100/18500 = 0.92^t . . . . divide by 18500
log(91/185) = t·log(0.92) . . . . take logarithms
t = log(91/185)/log(0.92) ≈ -0.3081/-0.03621 ≈ 8.509
It will be about 8.5 years until the value is $9100.
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Additional comment
The graph shows the solution to ...
18500·0.92^t -9100 = 0
We find it fairly easy to locate an x-intercept, so we wrote the equation in the forms that makes the x-intercept the solution.