Jack bought a new car in 2014 for 28,000. if the value of the car decreases by 14% each year, write an exponential model for the value of the car. then estimate the year the car will have a value of 5,000

In 2026 car will have a value of $5,000.

Step-by-step explanation:

We have been given that Jack bought a new car in 2014 for 28,000. If the value of the car decreases by 14% each year.

Since we know that an exponential function is in form: , where,

a = Initial value,

b = For decay or decrease b is in form (1-r), where r represents decay rate in decimal form.

Let us convert our given decay rate in decimal form.

Upon substituting a =28,000 and r=0.14 in exponential decay function we will get,

, where x represents number of years after 2014.

Therefore, the function represents the value of car x years after 2014.

To find the number of years it will take to car have the value of $5,000, we will substitute y=5,000 in our function.

Let us divide both sides of our equation by 28,000.

Let us take natural log of both sides of our equation.

Using natural log property we will get,

As in the 12th year after 2014 car will have a value of $5,000, so we will add 12 to 2014 to find the year.

Therefore, in 2026 car will have a value of $5,000.