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Answer:
(c) 5 years
Step-by-step explanation:
A graphing calculator shows the function ...
f(t) = 16000(1 -0.35)^t -2000
will be zero for t ≈ 4.83 years. Rounded to the nearest year, the value is expected to be about $2000 after 5 years.
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Using a scientific calculator, you can rewrite the equation to make use of logarithms.
2000 = 16000(1 -0.35)^t
2000/16000 = 0.65^t
log(1/8) = t·log(0.65)
t = log(0.125)/log(0.65) ≈ 4.827
Devon's car will be about 5 years old when its value is $2000.
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Additional comment
We expected to see the same sort of formula for continuous depreciation that we see for continuous growth: 2000 = 16000e^(-rt). The value formula given in the problem statement is a continuous function, but it should not be described as modeling continuous depreciation.
