Question

You purchase a car from a dealership for $15,000. The trade-in value of the car x years after the purchase is given by the function f(x) = 15,000 - 300x^2.

a. What type of function could be used to model the data?
b. After how many years will the trade-in value be $0
c. In this situation, what is the domain and range?

Answer 1

quadratic function

50 years

don’t know last one

Answer 2

a. Quadratic function is used to model the data

b. Trade in value will be 0 after sqrt(50) years or slightly more than 7 years

c. Domain: [0 , ∞] , Range: [-∞,15000]

Explanation:

The purchase price of the car is $15,000.

a. Trade value of the car x years after the purchase is represented by f(x) = 15000 - 300x^2.

This is a quadratic function which is used to represent the data.

b. Trade value will be 0 when 15000 - 300x^2 = 0

=> 300 x^2 = 15000

=> x^2 = 50

=> x= square root of 50 or
`√(x) 50`

c. Domain of x corresponds to all valid values of number of years post purchase, that is [0,∞]

Range of the function varies from [-∞ to 15000]