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.
(SHOW WORK)

Answer 1

Part 1) Australia
`19,751,012\ people`

Part 2) China
`1,319,645,764\ people`

Part 3) Mexico
`109,712,539\ people`

Part 4) Zaire
`60,534,681\ people`

Explanation:

we know that

The equation of a exponential growth function is given by

`P(t)=a(1+r)^t`

where

P(t) is the population

t is the number of years since year 2000

a is he initial value

r is the rate of change

Part 1) Australia

we have

`a=19,169,000\\r=0.6\%=0.6\100=0.006`

substitute

`P(t)=19,169,000(1+0.006)^t`

`P(t)=19,169,000(1.006)^t`

Find the expected population in 2025,

Find the value of t

t=2005-2000=5 years

substitute the value of t in the equation

`P(5)=19,169,000(1.006)^5=19,751,012\ people`

Part 2) China

we have

`a=1,261,832,000\\r=0.9\%=0.9\100=0.009`

substitute

`P(t)=1,261,832,000(1+0.009)^t`

`P(t)=1,261,832,000(1.009)^t`

Find the expected population in 2025,

Find the value of t

t=2005-2000=5 years

substitute the value of t in the equation

`P(5)=1,261,832,000(1.009)^5=1,319,645,764\ people`

Part 3) Mexico

we have

`a=100,350,000\\r=1.8\%=1.8\100=0.018`

substitute

`P(t)=100,350,000(1+0.018)^t`

`P(t)=100,350,000(1.018)^t`

Find the expected population in 2025,

Find the value of t

t=2005-2000=5 years

substitute the value of t in the equation

`P(5)=100,350,000(1.018)^5=109,712,539\ people`

Part 4) Zaire

we have

`a=51,965,000\\r=3.1\%=3.1\100=0.031`

substitute

`P(t)=51,965,000(1+0.031)^t`

`P(t)=51,965,000(1.031)^t`

Find the expected population in 2025,

Find the value of t

t=2005-2000=5 years

substitute the value of t in the equation

`P(5)=51,965,000(1.031)^5=60,534,681\ people`