Question

A car bought for $13,000 depreciates at a rate of 15% per year. Use an exponential function to find the value of the car after 5 years.

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Answer 1

$ 11093

Step-by-step explanation:

Recall that the formula for compound interest is:

A = P ( 1 + r/ n ) n ( t )

−−−−−−−−−−−−−−−−−−−−−−

where:

A = future value

P = principal (starting) amount

r = annual interest rate, expressed as a decimal

n = number of times the interest is compounded in a year

t = number of years compound interest occurs for

1 . Start by substituting your known values into the formula. Note that the annual interest rate is − 0.15 since the car depreciates (becomes lower in value) each year.

A = 25000 ( 1 + − 0.15 1 ) 1 ( 5 )

2 . Solve for A .

A = 25000 ( 0.85 ) )5

A = 11092.63

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

A ≈ $ 11093 a

−−−−−−−−−−−−−−−

Answer 2

Answer is $5,768.17

Step-by-step explanation:

Equation is as follows:

13,000(1-0.15)^5 =

13000(0.85)^5 = 13000x0.44370531 = 5,768.17 (rounds up)

.