a town has a population of 14000 and grows at 3% every year. what will be the population after 6 years, to…

Explanation:

Step1: Recall the compound growth formula

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. Here, ( P_0 = 14000 ), ( r = 0.03 ) (since 3% = 0.03), and ( t = 6 ).

Step2: Substitute the values into the formula

Substitute ( P_0 = 14000 ), ( r = 0.03 ), and ( t = 6 ) into ( P(t) = P_0(1 + r)^t ): ( P(6) = 14000(1 + 0.03)^6 )

Step3: Calculate ( (1 + 0.03)^6 )

First, calculate ( 1.03^6 ). Using a calculator, ( 1.03^6 \approx 1.1940522965 )

Step4: Multiply by the initial population

Multiply 14000 by 1.1940522965: ( P(6) = 14000 \times 1.1940522965 \approx 16716.732151 )

Step5: Round to the nearest whole number

Rounding 16716.732151 to the nearest whole number gives 16717.

Answer:

16717