a town has a population of 5000 and grows at 3.5% every year. what will be the population after 15 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 annual growth rate (as a decimal), and ( t ) is the number of years. Here, ( P_0 = 5000 ), ( r = 0.035 ) (since ( 3.5% = \frac{3.5}{100}=0.035 )), and ( t = 15 ).

Step2: Substitute the values into the formula

Substitute ( P_0 = 5000 ), ( r = 0.035 ), and ( t = 15 ) into ( P(t)=P_0(1 + r)^t ): ( P(15)=5000\times(1 + 0.035)^{15} )

Step3: Calculate ( (1 + 0.035)^{15} )

First, calculate ( 1+0.035 = 1.035 ). Then, find ( 1.035^{15} ). Using a calculator, ( 1.035^{15}\approx1.675348 )

Step4: Calculate the final population

Multiply ( 5000 ) by ( 1.675348 ): ( P(15)=5000\times1.675348 = 8376.74 )

Step5: Round to the nearest whole number

Rounding ( 8376.74 ) to the nearest whole number gives ( 8377 ).

Answer:

( 8377 )