Questions: Tacoma's population in 2000 was about 200 thousand, and has been growing by about 9% each year. If this continues, what will Tacoma's population be in 2013? thousand people

Tacoma's population in 2000 was about 200 thousand, and has been growing by about 9% each year. If this continues, what will Tacoma's population be in 2013?
thousand people

Transcript text: Tacoma's population in 2000 was about 200 thousand, and has been growing by about $9 \%$ each year. If this continues, what will Tacoma's population be in 2013? $\square$ thousand people

Solution

Solution Steps

Step 1: Convert the Annual Growth Rate

The annual growth rate given is 9%. To use it in our calculations, we convert it into a decimal by dividing by 100. Thus, the growth rate, $r$, is 0.09.

Step 2: Calculate the Future Population

Using the formula $P_{n} = P_{0}(1 + r)^{n}$, where $P_{0}$ is the initial population, $r$ is the annual growth rate in decimal form, and $n$ is the number of years into the future, we can calculate the future population. Substituting the given values, we get $P_{n} = 200 * (1 + 0.09)^{13}$.

Step 3: Round the Result

After calculating the future population, we round the result to 0 decimal places as required. This gives us a future population of 613.