Question

A country's population in 1993 was 94 million. in 1999 in was 99 million. estimate the population in 2005 using the exponential growth formula. round your answer to the nearest million. P=Ae^kt

Answer 1

The initial population is
P₀ = 94 million in 1993

The growth formula is

`P(t) = P_(0)e^(kt)`
where P(t) is the population (in millions) after t years, measured from 1993.
k = constant.

Because P(5) = 99 million (in 1999),

`94e^(5k) = 99 \\e^(5k)=1.0532 \\ 5k = ln(1.0532) \\ k = 0.010367`

In the year 2005, t = 12 years, and

`P(12)=94e^(0.010367*12) = 106.45`

Answer: 106 million (nearest million)