Answer:
13.2 years
Step-by-step 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.
