Math Help Growth Model

Question

In 2016 the United States had a population of about 323 million people and was growing at 0.7 %. Use an explicit exponential model to predict what year the U.S. population will reach 400 million people

Round to the nearest year

Answer 1

Let P_o = the initial population

P = population over time

P1 = population after the first year etc

Po = 323 million

P1 = (323 million) x (1.007)

P2 = (323 million)x(1.007)2 and so on .... therefore the general equation is Pn = (323 million)(1.007)n

The population reaches 400 million when Pn = 400 million So,

400 = 323(1.007)n Solving for n (years) we find that n = 30.65 years or 31 years