Question

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 ANSWER

C. −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!

Answer 1

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

`V = 12000 e^{ (k)/(100)t}`

Therefore

`12000 e^{ (k)/(100) (12)} = 11280 \\ e^(0.12k)= (11280)/(12000) =0.94\\ 0.12k=ln(0.94)\\k= (ln(0.94))/(0.12) =-0.5156`

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