Question

The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the expected population of each country in 2025, assuming their annual growth rates remain steady. Please show how to solve the problem.

Answer 1

After 25 years the population will be:

• Australia: 22271200
• China: 1580220878
• Mexico: 157380127
• Zaire: 112794819

Explanation:

Growth rate problem that has a growth rate proportional to the population size can be solved using the equation:

P(t) = P₀eʳᵗ

• t is your unit of time. It could be days, or hours, or minutes. It changes depending on each problem. In this problem, t is measured in years because you're jumping from 2000 to 2025. Years just makes the most sense to measure that leap in time.

• P(t) is the population at time t. An example in this problem could be P(20) would be the population 20 years after the initial count. or maybe P(12) would be the population 12 years after the initial count. or P(0) would be the initial count of the population.

• P₀ is the initial population at P(0)
• r is the growth rate. Don't forget to convert the percentage to its decimal form

Now that everything is set out, lets use the equation to solve for our answer.

P(t) = P₀eʳᵗ

Australia:

`P(t)=(19169000)e^((0.006)t)`

after 25 years

`P(25)=(19169000)e^((0.006)(25))=22271200.6`

China:

`P(t) = (1261832000)e^((.009)t)`

after 25 years:

`P(25)=(1261832000)e^((.009)(25))=1580220878`

Mexico:

`P(t) = (100350000)e^((0.018)t)`

after 25 years:

`P(25)=(100350000)e^((0.018)(25))=157380127.8`

Zaire:

`P(t) = (51965000)e^((0.031)t)`

after 25 years:

`P(25)=(51965000)e^((0.031)(25))=112794819.9`