Answer to Question #157776 in Calculus for Jonathan

Question

1.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?

Answer 1

$\text{let }p_0 = 12000\text{ city population}$

$\text{then the population of the city in 1 year}$

$p_1= p_0+p_0*\frac{3.5}{100}= p_0*\frac{103.5}{100}=p_0*1.035$

$\text{then the population of the city in 2 year}$

$p_2 = p_1*1.035=p_0*(1.035)^2$

$\text{then the population of the city in n year}$

$p_n = p_0*(1.035)^n$

$\text{then the population of the city in 7 year}$

$p_7 = p_0*(1.035)^7= 12000*(1.035)^7\approx15267$

Answer:15267