A new automobile costs $32,000. The value of the same automobile after t years is given by V = 32000(0.8)t. The following steps determine how many years it will take for the value to decrease to one-eighth the initial value, which is $4,000.
1)weneedtocompute(0.8)t=1/8
,sowetakelogarithmofbase10onboth side: write out the result.
2) using the fact that log102 = 0.3010, compute log108. [hint: 23 = 8]
3) use the result of log108, compute log10 (1/8). [hint: 1/8 = 8-1]
4) use the result of log108, compute log100.8 [hint: 0.8 = 8/10]
5) use the result of 3) and 4), solve for t in 1)
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