F(x) = 15,000(.84) shows the value of a car each year. Describe the following: a) What does 15,000 in this story problem?
b) What is the growth/decay percent rate in this story problem?
c) What does x represent in this story problem?
d) What does f(x) represent in this story problem?

Answers:

Explanation:

We have the function f(x) = 15000(0.84)^x. If we plug in x = 0, then we get,

f(x) = 15000(0.84)^x

f(0) = 15000(0.84)^0

f(0) = 15000(1)

f(0) = 15000

In the third step, I used the idea that any nonzero value to the power of 0 is always 1. The rule is x^0 = 1 for any nonzero x.

So that's how we get the initial value of the car. The car started off at $15,000.

The growth or decay rate depends entirely on the base of the exponential, which is 0.84; compare it to 1+r and we see that 1+r = 0.84 solves to r = -0.16 which converts to -16%. The negative indicates the value is going down each year. So we have 16% decay or the value is going down 16% per year.

The value of x is the number of years. In the first section, x = 0 represented year 0 or the starting year. If x = 1, then one full year has passed by. For x = 2, we have two full years pass by, and so on.

The value of f(x) is the value of the car after x years have gone by. We found that f(x) = 15000 when x = 0. In other words, at the start the car is worth $15,000. Plugging in other x values leads to other f(x) values. For example, if x = 2, then you should find that f(x) = 10584. This means the car is worth $10,584 after two years.