Question

A new car is purchased for 19900 dollars. The value of the car depreciates at 7.5% per year. What will the value of the car be, to the nearest cent, after 8 years?

Answer 1

Answer: The answer is 10665.64

Explanation:

Exponential Functions:

y=ab^x

A= starting value = 19900

r=rate = 7.5%=0.075

Exponential Decay:

b=1-r=1-0.075=0.925

Write Exponential Function:

y=19900(0.925)^x

Plug in time for x:

y=19900(0.925)^8

y= 10665.6404317

Evaluate

y≈10665.64

Answer 2

`\$10,665.64`

Explanation:

we know that

The formula to calculate the depreciated value is equal to

`V=P(1-r)^(x)`

where

V is the depreciated value

P is the original value

r is the rate of depreciation in decimal

x is Number of Time Periods

in this problem we have

`P=\$19,900\\r=7.5\%=0.075\\x=8\ years`

substitute the values in the formula

`V=\$19,900(1-0.075)^(8)=\$10,665.64`