A town has a population of 17000 and grows at \( 3 \% \) every year. What will be the population after 7 years, to the nearest whole number?

To find the population after 7 years, we can use the formula for exponential growth: \[ P(t) = P_0 \times (1 + r)^t \] where: - \( P(t) \) is the population after \( t \) years, - \( P_0 \) is the initial population, - \( r \) is the annual growth rate, - \( t \) is the number of years. Given: - Initial population \( P_0 = 17000 \), - Annual growth rate \( r = 3\% = 0.03 \), - Number of years \( t = 7 \). Substitute the values into the formula: \[ P(7) = 17000 \times (1 + 0.03)^7 \] Now, we can calculate the population after 7 years. Calculate the value by following steps: - step0: Calculate: \(17000\left(1+0.03\right)^{7}\) - step1: Add the numbers: \(17000\times 1.03^{7}\) - step2: Convert the expressions: \(17000\left(\frac{103}{100}\right)^{7}\) - step3: Simplify: \(17000\times \frac{103^{7}}{100^{7}}\) - step4: Rewrite the expression: \(1000\times 17\times \frac{103^{7}}{100^{7}}\) - step5: Rewrite the expression: \(10^{3}\times 17\times \frac{103^{7}}{10^{14}}\) - step6: Reduce the numbers: \(17\times \frac{103^{7}}{10^{11}}\) - step7: Multiply: \(\frac{17\times 103^{7}}{10^{11}}\) The population after 7 years will be approximately 20907.855712. Rounding this to the nearest whole number, the population after 7 years will be approximately 20908.