Question

A country's population in 1990 was 132 million. In 1998, 137 million. Estimate the population in 2003. (exponential growth, P=Ae^kt, round k four decimal places)

Answer 1

Plug-in for t=0 to solve for A:
132 = Ae^k(0)
A = 132
in 1998, t=1998-1990=8 years and population P=137 million, plug-in values to solve for k:
137 = 132e^8k
137/132 = e^8k = 1.038
Applying ln on both sides to cancel e:
8k = ln 1.038
k = 0.0046
Estimating population in 2003:
t = 2003 - 1990 = 13 years
Therefore
P(2003) = 132e^(0.0046*13)
P(2003) = approx 140.13 million // answer