A town has a population of 12000 and grows at \( 3.5 \% \) 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 compound interest, which is given by: \[ P = P_0 \times (1 + r)^n \] Where: - \( P \) is the final population after \( n \) years - \( P_0 \) is the initial population - \( r \) is the growth rate per year - \( n \) is the number of years Given: - \( P_0 = 12000 \) (initial population) - \( r = 3.5\% = 0.035 \) (growth rate per year) - \( n = 7 \) (number of years) Substitute these values into the formula and calculate the final population after 7 years. Calculate the value by following steps: - step0: Calculate: \(12000\left(1+0.035\right)^{7}\) - step1: Add the numbers: \(12000\times 1.035^{7}\) - step2: Convert the expressions: \(12000\left(\frac{207}{200}\right)^{7}\) - step3: Simplify: \(12000\times \frac{207^{7}}{200^{7}}\) - step4: Rewrite the expression: \(200\times 60\times \frac{207^{7}}{200^{7}}\) - step5: Reduce the numbers: \(60\times \frac{207^{7}}{200^{6}}\) - step6: Rewrite the expression: \(20\times 3\times \frac{207^{7}}{200^{6}}\) - step7: Rewrite the expression: \(20\times 3\times \frac{207^{7}}{20^{6}\times 10^{6}}\) - step8: Reduce the numbers: \(3\times \frac{207^{7}}{20^{5}\times 10^{6}}\) - step9: Multiply the fractions: \(\frac{3\times 207^{7}}{20^{5}\times 10^{6}}\) The population after 7 years will be approximately 15267.35. Rounding this to the nearest whole number, the population will be 15267.