Questions: 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 2015? thousand people

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 2015? thousand people
Transcript text: Question 3 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 2015? $\square$ thousand people Question Help: Message instructor
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Solution

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Solution Steps

Step 1: Convert the Annual Growth Rate to a Decimal

To convert the annual growth rate from a percentage to a decimal, we divide the given rate by 100. Thus, \(r = \frac{8}{100} = 0.08\).

Step 2: Calculate the Future Population

Using the formula \(P = P_0 \times (1 + r)^t\), where \(P_0 = 200\), \(r = 0.08\), and \(t = 15\), we calculate the future population. Substituting the values, we get \(P = 200 \times (1 + 0.08)^15 = 634\).

Final Answer:

The future population of the city, rounded to 0 decimal places, is 634.

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