Exponential decay occurs when the quantity of something decreases at a rate that is proportional to its current value. For example, a population of animals might decay as their habitat is slowly eroded by human encroachment, or the amount of radiation that is emitted from a radioactive substance could decrease as time passes.

Suppose that your friend Rhyley has saved $5,000 toward the cost of a car and her parents have agreed to match that amount, dollar for dollar. You learned in your algebra 2 class that the value of a car decreases as time passes. You want to use your knowledge to help your friend buy the best car that she can with the money she has available. Rhyley has narrowed the options down to two different cars, both of which have similar features:

Car A

Cost: $8,750

Mileage: 89,325

Year of Manufacture: 2015

Decay Factor (average): 12%

Car B

Cost: $9,995

Mileage: 73,498

Year of Manufacture: 2017

Decay Factor (average): 18%

Use the information given and your knowledge of exponential decay to help your friend Rhyley by answering the questions below.

1. Write a exponential decay function in the form for each of Car A and Car B. Explain how you determined the value of b for each function.

f(x)= 8,750x0.88^x for car A

f(x)=9,995x0.82^x for car B

You take the percent decay and subtract it from 100% then convert it into a decimal.

After some consideration, Rhyley's best guess is that she will own the car she chooses for 5 years. Explain two different ways you could determine the value of each car in the fifth year Rhyley owns it. I've got the first way but I need help with the second way.

Putting 5 into the x value of the functions f(x)=8750x.88^x and f(x)=9995x.82^x

Rhyley still cannot decide which car she really wants. Beyond the cost, mileage, and how the value of the car decreases, what are some other factors Rhyley might consider when making her decision?