Question

the manufacturers suggested retail price (msrp) for a particular car is $25,430, and it is expected to be worth $19,970 in 2 years
(a) find a linear depreciation function for this car.
(b) estimate the value of the car 3 years from now.
(c) at what rate is the car depreciating?
(a) what is the linear depreciation function for this car?
f(x)=\square
(simplify your answer. do not include the $ symbol in your answer.)

Explanation:

Step1: Define linear function form

A linear function is \( f(x)=mx + b \), where \( x \) is time (years), \( m \) is slope (depreciation rate), and \( b \) is initial value. Initial value \( b = 25430 \) (MSRP at \( x = 0 \)). At \( x = 2 \), \( f(2)=19970 \).

Step2: Calculate slope \( m \)

Use slope formula \( m=\frac{f(2)-f(0)}{2 - 0}=\frac{19970 - 25430}{2}=\frac{-5460}{2}=-2730 \).

Step3: Form linear function

Substitute \( m=-2730 \) and \( b = 25430 \) into \( f(x)=mx + b \). So \( f(x)=-2730x + 25430 \).

Answer:

\( f(x)=-2730x + 25430 \)