loses value over time. This is known as a depreciating asset. If you purchase a brand new pickup truck for $ \$ 80,000 $
$ 71,500(1+6)^{+20}=125,000 $ once you purchase in item like a car, it and it loses $ 15 \% $ of its value each year, when will its value be half of its original? (This means to find its half life) When will the vehicle be worth $ \$ 25,000 $ ?

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Answer

t' = \frac{\ln{(\frac{25000}{80000})}}{\ln{(1 - 0.15)}}

Steps

Step 1 ：V = 80000(1 - 0.15)^t

Step 2 ：\frac{80000}{2} = 80000(1 - 0.15)^t

Step 3 ：\ln{(\frac{1}{2})} = t \ln{(1 - 0.15)}

Step 4 ：t = \frac{\ln{(\frac{1}{2})}}{\ln{(1 - 0.15)}}

Step 5 ：25000 = 80000(1 - 0.15)^t'

Step 6 ：\frac{25000}{80000} = (1 - 0.15)^{t'}

Step 7 ：\ln{(\frac{25000}{80000})} = t' \ln{(1 - 0.15)}

Step 8 ：t' = \frac{\ln{(\frac{25000}{80000})}}{\ln{(1 - 0.15)}}