The equation of the exponential regression is [tex]\rm y = 14100 \ e^{-0.087x}[/tex]. And the value of a car after 15 years is $ 3,823.53.
What is an exponent?
Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
The accompanying table shows the value of a car over time that was purchased for 14100 dollars, where x is years and y is the value of the car in dollars.
The exponential regression equation will be given as
[tex]\rm y = A_o e^{kx}[/tex]
Where A₀ is the coefficient of exponential regression and k is the constant.
For x = 0, the value of y will be $ 14100. Then we have
[tex]\rm 14100= A_o e^{k*0}\\\\ A_o \ \ \ \ = 14100[/tex]
Then the equation will be
[tex]\rm y = 14100 \ e^{kx}[/tex]
For x = 1, the value of y will be $12,929. Then we have
[tex]\rm 12929= 14100 e^{k*1}\\\\ e^k \ \ \ \ = 0.91695[/tex]
Taking ln both sides, then we have
[tex]\begin{aligned} \rm ln\ e^k &= ln \ 0.91695\\\\\rm k*ln \ e &= -0.087\\\\\rm k &= -0.087 \end{aligned}[/tex]
Then the equation will be
[tex]\rm y = 14100 \ e^{-0.087x}[/tex]
Then after 15, the value of a car will be
[tex]\rm y = 14100 \ e^{-0.087*15}\\\\\rm y = 14100 * 0.2712\\\\\rm y = 3823.53[/tex]
More about the exponent link is given below.
https://brainly.com/question/5497425
