Question

In 2007 the population of the town of Cartersville was 24,455. The population growth can be represented by the formula P = 24,455(1.03)x, where x represents the number of years after 2007. When will the population of the town first exceed 30,000?

Answer 1

You would multiple by 1.03 until you reach 30000.2017

Answer 2

If
`P` represents population, and
`x` represents the number of years after 2007, then we need to set
`P` to
`30,000` and solve for
`x`, then add that to 2007.


`30000 = 24455(1.03)x \Longleftrightarrow 30000 = 25188.65x`

Now divide each side by
`25188.65` to solve for
`x`.


`x = 1.19`


`x` represents the number of years since 2007, so to get a year value, we need to add
`1.19` to 2007.

That gives you
`2008.119`. We don't represent years with decimals, so the answer would be 2008.