A town has a population of 10000 and grows at \( 5 \% \) every year. What will be the population after 5 years, to the nearest whole number? Answer Attempt out of 2

To calculate the population of the town after 5 years with an annual growth rate of 5%, we can use the formula for exponential growth: \[ P = P_0 (1 + r)^t \] where: - \( P \) is the future population, - \( P_0 \) is the initial population, - \( r \) is the growth rate (as a decimal), - \( t \) is the number of years. Given: - \( P_0 = 10000 \) - \( r = 0.05 \) - \( t = 5 \) Substituting the values into the formula: \[ P = 10000 (1 + 0.05)^5 \] Calculating \( (1 + 0.05)^5 \): \[ (1.05)^5 \approx 1.2762815625 \] Now, substituting this back into the equation for \( P \): \[ P \approx 10000 \times 1.2762815625 \approx 12762.815625 \] Rounding to the nearest whole number, the population after 5 years will be approximately: \[ \boxed{12763} \]