a town has a population of 12000 and grows at 5% every year. what will be the population after 12 years, to…

Explanation:

Step1: Identify the formula for compound growth

The formula for compound growth is ( P(t) = P_0(1 + r)^t ), where ( P_0 ) is the initial population, ( r ) is the growth rate (in decimal), and ( t ) is the time in years.

Step2: Convert the growth rate to decimal

The growth rate ( r = 5% = 0.05 ). The initial population ( P_0 = 12000 ), and time ( t = 12 ) years.

Step3: Substitute values into the formula

Substitute ( P_0 = 12000 ), ( r = 0.05 ), and ( t = 12 ) into the formula: ( P(12) = 12000(1 + 0.05)^{12} ).

Step4: Calculate the value

First, calculate ( (1.05)^{12} \approx 1.795856 ). Then, multiply by 12000: ( 12000 \times 1.795856 \approx 21550.27 ). Rounding to the nearest whole number gives 21550.

Answer:

21550