Question 13

Tacoma's population in 2000 was about 200 thousand, and has been growing by about $8 \%$ each year. If this continues, what will Tacoma's population be in 2020 ?
people
Check Answer

Step 1 ：The problem is asking for the population of Tacoma in 2020 given that it was 200 thousand in 2000 and it has been growing by 8% each year. This is a compound interest problem where the principal is the initial population, the rate is the annual growth rate, and the time is the number of years from 2000 to 2020.

Step 2 ：We can use the formula for compound interest which is: \(A = P(1 + \frac{r}{n})^{nt}\) where: \(A\) is the amount of money accumulated after n years, including interest, \(P\) is the principal amount (the initial amount of money), \(r\) is the annual interest rate (in decimal), \(n\) is the number of times that interest is compounded per year, and \(t\) is the time the money is invested for in years.

Step 3 ：In this case, the principal \(P\) is 200 thousand, the rate \(r\) is 8% or 0.08 in decimal, \(n\) is 1 since the population grows annually, and \(t\) is 20 years from 2000 to 2020.

Step 4 ：Let's plug these values into the formula and calculate the population in 2020: \(P = 200\), \(r = 0.08\), \(n = 1\), \(t = 20\), \(A = 932.1914287698617\)

Step 5 ：The result from the calculation is approximately 932.19. This means that the population of Tacoma in 2020 will be approximately 932.19 thousand or 932,190 people if it continues to grow by 8% each year from its population of 200 thousand in 2000.

Step 6 ：Final Answer: The population of Tacoma in 2020 will be approximately \(\boxed{932,190}\) people.