Question

The table below represents the value of a new car after the certain years. Time(years) 12345 Value of Car ($) 27400 21200 17000 14300 11100 Find your exponentiregression equation. What is the value of a?choose your answer...Is this a growth or decay function?choose your answer...What is the value of b?choose your answer...What is the value of the car after 18 years? choose your answer...choose your answer...What is the correlation of determination?When will the value of the car be $8100?choose your answer...

Answer 1

if we made the regrecion in a calculator or in Excel we can see that the equation will be:

$y=33558e^{-0.22x}$

and the formila of an exponent is:

$y=ae^{bx}^{}$

b is equal to -0.22

also b is negative so is decay function

the correlation is 33558

To find the value in 18 years we replace x equal to 18 so

$\begin{gathered} y=33558e^{-0.22(18)} \\ y=33558e^{-3.96} \\ y=33558(0.02) \\ y=679.28 \end{gathered}$

So in 18 years the value will be 679.28

Now for the final one we replace y for 8100 so:

$8100=33558e^{-0.22x}$

and we solve for x so:

$\begin{gathered} \frac{8100}{33558}=e^{-0.22x} \\ \ln (0.24)=-0.22x \\ \frac{-1.43}{-0.22}=x \\ x=6.4 \end{gathered}$

So in 6.4 years the cost will be 8100