Question

Maureen bought a new car worth $26,525 one year ago. She knows that her car's value will depreciate each year. She uses an online calculator to find that her car is worth $24,403 today. Write an exponential equation in the form y = a(b) that can model the value, y, of Maureen's car x years after purchase. Use whole numbers, decimals, or simplified fractions for the values of a and b. ​

Answer 1

The equation to model the value of Maureen's car x years after purchase can be written in the form of y = a(b)^x , where y is the value of the car, x is the number of years after purchase, and a and b are constants.

Using the information given, we can find the values of a and b.

We know that the value of the car one year after purchase is $24,403.

So, we can substitute this value into the equation:

24403 = a(b)^1

We also know that the car's original value is $26,525

So we can substitute this value into the equation:

26525 = a

Now we can use these two equations to find the value of b

24403 = 26525 (b)^1

b = 24403 / 26525

b = 0.9153

So the final equation is:

y = 26525 (0.9153)^x

where y is the value of the car, x is the number of years after purchase, and a = 26525 and b = 0.9153