Answer:
The populaton in year 1991 will be of 5178.9 million of people
and the population in year 2020 will be of 8524.60 million of people
Step-by-step explanation:
We measure the time t in years and let t=0 in the year 1950.
We measure the population P(t) in millions of people, then P(0)=2560 and P(10) = 3040.
Since we are assuming that dp/dt=kP, this theorem gives the following.
[tex]P(t) = P(0)e^{kt}= 2560e^{kt}[/tex]
[tex]P(10) = 2560 e^{10k} = 3040[/tex]
[tex]k=\frac{1}{10} ln (3040/2560) = 0.0171[/tex]
The relative growth rate is about 1.7% per year and the model is
[tex]P(t) = 2560e^{0.017185t}[/tex]
Year 1991 is equal in our formula to 41 and year 2020 is equal to 70. Replacing,
[tex]P(41) = 2560e^{0.017185(41)}=5178.89[/tex]
[tex]P(70) = 2560e^{0.017185(70)}=8524.60[/tex]
Therefore the populaton in year 1991 will be of 5178.9 million of people and the population in year 2020 will be of 8524.60 million of people
