Answer:
Part 1) Australia [tex]19,751,012\ people[/tex]
Part 2) China [tex]1,319,645,764\ people[/tex]
Part 3) Mexico [tex]109,712,539\ people[/tex]
Part 4) Zaire [tex]60,534,681\ people[/tex]
Step-by-step explanation:
we know that
The equation of a exponential growth function is given by
[tex]P(t)=a(1+r)^t[/tex]
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
[tex]a=19,169,000\\r=0.6\%=0.6\100=0.006[/tex]
substitute
[tex]P(t)=19,169,000(1+0.006)^t[/tex]
[tex]P(t)=19,169,000(1.006)^t[/tex]
Find the expected population in 2025,
Find the value of t
t=2005-2000=5 years
substitute the value of t in the equation
[tex]P(5)=19,169,000(1.006)^5=19,751,012\ people[/tex]
Part 2) China
we have
[tex]a=1,261,832,000\\r=0.9\%=0.9\100=0.009[/tex]
substitute
[tex]P(t)=1,261,832,000(1+0.009)^t[/tex]
[tex]P(t)=1,261,832,000(1.009)^t[/tex]
Find the expected population in 2025,
Find the value of t
t=2005-2000=5 years
substitute the value of t in the equation
[tex]P(5)=1,261,832,000(1.009)^5=1,319,645,764\ people[/tex]
Part 3) Mexico
we have
[tex]a=100,350,000\\r=1.8\%=1.8\100=0.018[/tex]
substitute
[tex]P(t)=100,350,000(1+0.018)^t[/tex]
[tex]P(t)=100,350,000(1.018)^t[/tex]
Find the expected population in 2025,
Find the value of t
t=2005-2000=5 years
substitute the value of t in the equation
[tex]P(5)=100,350,000(1.018)^5=109,712,539\ people[/tex]
Part 4) Zaire
we have
[tex]a=51,965,000\\r=3.1\%=3.1\100=0.031[/tex]
substitute
[tex]P(t)=51,965,000(1+0.031)^t[/tex]
[tex]P(t)=51,965,000(1.031)^t[/tex]
Find the expected population in 2025,
Find the value of t
t=2005-2000=5 years
substitute the value of t in the equation
[tex]P(5)=51,965,000(1.031)^5=60,534,681\ people[/tex]
