Tacoma's population in 2000 was about 200,000 people, and has been growing by about \( 8 \% \) each year. If the population continues to grow according to the model \( P_{n}=P_{0}(1+r)^{n} \). what will Tacoma's population be in 2015 ? Round the estimated population to the nearest thousand. people Substion Help: Qvideo

To find the population of Tacoma in 2015, we can use the given population growth model: \[ P_{n} = P_{0}(1 + r)^{n} \] Given: - Initial population in 2000, \( P_{0} = 200,000 \) people - Annual growth rate, \( r = 8\% = 0.08 \) - Year for which we want to find the population, \( n = 2015 - 2000 = 15 \) years Substitute the given values into the model: \[ P_{15} = 200,000(1 + 0.08)^{15} \] Now, we can calculate the population of Tacoma in 2015 using the given model. Calculate the value by following steps: - step0: Calculate: \(200000\left(1+0.08\right)^{15}\) - step1: Add the numbers: \(200000\times 1.08^{15}\) - step2: Convert the expressions: \(200000\left(\frac{27}{25}\right)^{15}\) - step3: Simplify: \(200000\times \frac{27^{15}}{25^{15}}\) - step4: Rewrite the expression: \(3125\times 64\times \frac{27^{15}}{25^{15}}\) - step5: Rewrite the expression: \(5^{5}\times 64\times \frac{27^{15}}{5^{30}}\) - step6: Reduce the numbers: \(64\times \frac{27^{15}}{5^{25}}\) - step7: Multiply: \(\frac{64\times 27^{15}}{5^{25}}\) The population of Tacoma in 2015 will be approximately 634,433.82 people. Rounding this to the nearest thousand, the estimated population of Tacoma in 2015 will be approximately 634,000 people.