Question

An automobile originally purchased for $18,000 is losing value at a rate of 15% per year. The number of dollars it will be worth 5 years after purchase is 18,000(0.85)^5. Rewriting the expression 18,000(0.85)^5 in which of these ways would be useful in calculating the rate at which it is losing value per month?

A. 18,000(0.85^1/12)^60
B. 18,000(0.85^12)^60
C. 18,000(0.85^60)^1/12
D. 18,000(0.85^60)^12

Answer 1

Option A,
`18,000(0.85^1/12)^60,` is the correct way to calculate the rate at which the automobile is losing value per month.

Step-by-step explanation:

The expression
`18,000(0.85)^5` can be rewritten to calculate the rate at which the automobile is losing value per month as follows:

A.
`18,000(0.85^1/12)^60`

The correct answer is option A. By raising 0.85 to the power of 1/12, we capture the monthly rate, and then raising it to the power of 60 accounts for the number of months in 5 years.

Multiplying this value by the original value of $18,000 gives us the rate at which the automobile is losing value per month.

Answer 2

b

Step-by-step explanation: