Autumn is thinking about buying a car. the table below shows the projected value of two different cars for three years.

number of years 1 2 3
car 1 (value in dollars) 38,000 32,000 26,000
car 2 (value in dollars) 38,000 32,300 27,455

part a: what type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? explain your answer. (2 points)

part b: write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)

part c: autumn wants to purchase a car that would have the greatest value in 6 years. will there be any significant difference in the value of either car after 6 years? explain your answer, and show the value of each car after 6 years. (4 points)

*especially b pls

Part A:

A linear function is used for a series with a common difference while an exponential function is used for a series with a common ratio

The series for car 1 is 38000, 32000, 26000 which has a common difference of 6000 since the value decreases by 6000 every year.

The series for car 2 is 38000, 32300, 27455 which has a common ratio of . The common ratio is worked out from  and if we compare the 2nd term to the 3rd term we should get the same ratio 

Hence, linear function is more suitable for Car 1 and exponential function for Car 2

Part B:

A linear function is given by  where
= value after  year
= number of years
= the common difference
= the value of the  term

For Car 1, we have  and , so the equation is 

An exponential function is given by the form  where
=the value after  years
= the number of years
=the value of the first term
= the common ratio

For Car 2 we have  and , so the equation is . When using this formula, make sure to calculate first the  then multiply by 38000

Part C:

The exponential function will give slower rate of  growth/decay compared to a linear function

Value for Car 1 after 6 years


Value for Car 2 after 6 years