Needshow and explain your answer! autumn is thinking about buying a car for $38,000. 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) 32,000 26,000 20,000 car 2 (value in dollars) 32,300 27,455 23,336.75 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. part b: write one function for each car to describe the value of the car f(x), in dollars, after x years. part c: autumn wants to purchase a car that would have the greatest value in 5 years. will there be any significant difference in the value of either car after 5 years? explain your answer, and show the value of each car after 5 years.

A. The decrease in Car 1 value is constant at 6000 from year to year. Its value can be described by a linear function.

The decrease in Car 2 value is a constant percentage of its current value from year to year. Its value can be described by an exponential function.

B. The slope of the Car 1 function is -6000, and the value is 32000 in year 1, so the value function for Car 1 can be written as

... f(x) = 32000 -6000(x-1)

... f(x) = 38000 -6000x

The value multiplier for Car 2 from year to year is 27455/32300 = 0.85, so the value function for Car 2 can be written as

... f(x) = 32,300·0.85^(x-1)

... f(x) = 38000·0.85^x

C. There is a significant difference in value after 5 years. Car 2 is worth more than double the value of Car 1 in year 5. That year, their values are ...

... car 1: $8000

... car 2: $16861

560

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