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The​ manufacturer's suggested retail price​ (MSRP) for a particular car is ​$​24810, and it is expected to be worth ​$19254 in 2 years.

​(a) Find a linear depreciation function for this car.

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Final answer:

To find the linear depreciation function for the car, use the formula y = mx + b. Given the MSRP and the expected value in 2 years, calculate the slope and y-intercept to obtain the depreciation function.

Step-by-step explanation:

To find the linear depreciation function for the car, we can use the formula for the equation of a straight line: y = mx + b, where y represents the value of the car, x represents the number of years, m represents the depreciation rate, and b represents the initial value.

Given that the MSRP is $24,810 and the car is expected to be worth $19,254 in 2 years, we can use these points to find the slope (m) and the y-intercept (b).

Slope (m) = (y2 - y1) / (x2 - x1) = (19,254 - 24,810) / (2 - 0) = -2,578

Plugging in the values for m and b into the equation, we can find the depreciation function: y = -2,578x + 24,810

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