Question

Consider the exponential function

f(x)=19,000•0.96x, which models the value of Mark’s car, where x represents the number of years since he purchased the car.

What is the approximate value of Mark’s car after 7 years rounded to the nearest dollar?

a $14,278
b $14,000
c $14,277
d $14,280

Answer 1

a) 14,278

Explanation:

19000 × 0.96⁷

14277.50208

Answer 2

Given:

The given function
`f(x)=19,000 \cdot 0.96 ^x` which models the value of Mark’s car, where x represents the number of years since he purchased the car.

We need to determine the approximate value of Mark's car after 7 years.

Value of the car:

The value of the car after 7 years can be determined by substituting x = 7 in the function
`f(x)=19,000 \cdot 0.96 ^x`, we get;

`f(7)=19,000 \cdot 0.96 ^7`

`f(7)=19,000 \cdot 0.7514474781`

`f(7)=14277.502`

Rounding off to the nearest dollar, we get;

`f(7)=14278`

Thus, the approximate value of Mark's car after 7 years is $14278.

Hence, Option a is the correct answer.