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.