Given:
The given function [tex]f(x)=19,000 \cdot 0.96 ^x[/tex] 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 [tex]f(x)=19,000 \cdot 0.96 ^x[/tex], we get;
[tex]f(7)=19,000 \cdot 0.96 ^7[/tex]
[tex]f(7)=19,000 \cdot 0.7514474781[/tex]
[tex]f(7)=14277.502[/tex]
Rounding off to the nearest dollar, we get;
[tex]f(7)=14278[/tex]
Thus, the approximate value of Mark's car after 7 years is $14278.
Hence, Option a is the correct answer.
