Question

In 2007, there were more than 8.14 million cars for sale. The number of cars then decreased by 23% per year. Write an exponential growth or decay model given by the number of c cars over t years after 2007. Use this model to estimate how many cars there were in 2013?

Answer 1

In 2013 there were approximately 2.2 million cars for sale.

Explanation:

Since the number of cars is decreasing by 23% per year, it is a decay model. This types of decay can be expressed in the following expression:

`cars(x) = cars(2007)*(1 - 0.23)^(x - 2007)`

Where x is the year, cars(2007) is the number of cars in 2007. Applying this data we have:

`cars(x) = 8.14*(0.77)^(x - 2007)`

If we want to know the number of cars in 2013, we need to apply that value to x and solve the expression.

`cars(2013) = 8.14*(0.77)^(2013 - 2007)\\cars(2013) = 8.14*(0.77)^(5) = 2.20332`

In 2013 there were approximately 2.2 million cars for sale.