contestada

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. āˆ’0.005143%

B. āˆ’0.5143% <------ CORRECT ANSWER

C. āˆ’0.005%

D. āˆ’0.5%

I LOOKED EVERYWHERE FOR THIS ANSWER AND COULDN'T FIND IT, I TOOK THE TEST AND THIS WAS THE CORRECT ANSWER!

Respuesta :

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

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

Therefore
[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:Ā  k = -0.5156%
Note that a different decay function will yieldĀ a slightly different answer.

Otras preguntas