Question

A countrys population in 1991 was 147 million. In 1998 it was 153 million. Estimate the population in 2017 using exponential growth formula. Round your answer to the nearest million. P=Ae to the power kt

Answer 1

Answer:

171 million

Step-by-step explanation:

Given the exponential growth formula expressed as $P = Ae^{kt}$ where P is the countrys population and t is the time.

Initially in 1991, at t= 0, P = 147 million

$P = Ae^{kt}\\147 = Ae^{k(0)}\\147 = Ae^0\\147 = A(1)\\A = 147$

If by 1998 it was 153 million, this means that the population is 153 million 7 years later i.e when t = 7, P = 153. On substituting into the formula to get the constant 'k';

$P = Ae^{kt}\\153 = 147e^{k(7)}\\153 = 147e^{7k}\\153/147 = e^{7k}\\e^{7k} = 1.041\\Taking \ ln \ of \ both \ sides\\lne^{7k} = ln 1.041\\7k = 0.04018\\k = 0.04018/7\\k = 0.00574$

To estimate the population in 2017, to number of years from 1991 to 2017 is 26 years. Hence we are to find the value of P given t = 27, A = 147 and k = 0.00574

$P = Ae^{kt}\\P = 147e^{0.00574*26}\\P = 147e^0.14924\\P = 147*1.16095\\P = 170.659$

Hence the population in 2017 using exponential growth formula to the nearest million is 171 million.