Question

A country's population in 1990 was 123 million. In 2002 it was 128 million. Estimate the population in 2013 using the exponential growth formula. Round your answer to the nearest million.

Answer 1

R=(128÷123)^(1÷12)-1
R=0.0033

P=128(1.0033)^(2013-2002)
P==132.72 million

Answer 2

Population in 2013 is 132.76 ≈ 133 million.

Explanation:

A country's population in 1990 was 123 million

In 2002 it was 128 million.

We have to calculate the population in 2013.

Since population growth is always represented by exponential function.

It is represented by
`P(t)=P_(0)e^(kt)`

Here t is time in years, k is the growth constant, and
`p_(0)` is initial population.

For year 1990 ⇒

128 =
`P_(0)e^(12k)` =
`123e^(12k)`

`(128)/(123)=e^(12k)`

taking ln on both the sides ⇒

ln
`((128)/(123))= lne^(12k)`

ln 128 - ln 123 = 12k [since ln e = 1 ]

4.852 - 4.81218 = 12 k

k =
`(0.03985)/(12)=0.00332`

For year 2013 ⇒

`P(t)=P_(0)e^(kt)`

`P(t)=123.e^((0.00332)(23))`

= 123 ×
`e^(0.07638)`

= 123 × 1.07937

= 132.76 rounded to 133 million.

Therefore, population in 2013 is 132.76 ≈ 133 million.