A motorcycle cost $12,000 when it was purchased. The value of a motorcycle decreases by 6% each year. Find the rate of decay each month and select the correct answer below.A. −0.005143%B. −0.5143% <------ CORRECT ANSWERC. −0.005%D. −0.5%I LOOKED EVERYWHERE FOR THIS ANSWER AND COULDN'T FIND IT, I TOOK THE TEST AND THIS WAS THE CORRECT ANSWER!

Accepted Solution

The original cost is $12000.
The value decreases by 6% in 12 months (1 year), so the cost after 12 months is
(1 - 0.06)*12000 = $11,280

Let  k =  the percent rate of decay each month
Let  t =  months
Model the value as
[tex]V = 12000 e^{ \frac{k}{100}t} [/tex]

[tex]12000 e^{ \frac{k}{100} (12)} = 11280 \\ e^{0.12k}= \frac{11280}{12000} =0.94\\ 0.12k=ln(0.94)\\k= \frac{ln(0.94)}{0.12} =-0.5156[/tex]

Answer:  k = -0.5156%
Note that a different decay function will yield a slightly different answer.