Question

The value of a brand new car is $40,000 and the value depreciates 23% every year. Write a function to represent the value of the car after t years, where the monthly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per month, to the nearest hundredth of a percent.

Answer 1

The function to represent the value of the car after t years is V(t) = 40,000 * (1 - 0.23)^t

The coefficient of the function is 0.77 (1- 0.23)

To find the rate of change per month, we need to find the rate at which the value of the car is decreasing each month.

we can use the rule of 72

72/r = t where r is the rate of change per month

r = 72/t

r = 72/23 = 3.13 (approx)

So the percentage rate of change per month is 3.13%

So, The function to represent the value of the car after t years is V(t) = 40000(0.77^t) and the percentage rate of change per month is 3.13%

Explanation: