Answer:
By 2086
Step-by-step explanation:
The provided equation is:
[tex]A=A0*e^{k*t}[/tex] , where:
A=total of population after t years
A0=initial population
k= rate of growth
t= time in years
Given information:
The final population will be 15 million, then A=15.
We start in 2000 with a 5.82 million population, then A0=5.82.
Missing information:
Although k is not given, we can calculate k by using the following statement, from 2000 to 2040 (within 40 years) population is proyected to grow to 9 million, which means a passage from 5.8 to 9 million (3.2 million increament).
Then we can use the same expression to calculate k:
[tex]A=A0*e^{k*t}[/tex]
[tex]9=5.8*e^{40*k}[/tex]
[tex]ln(9/5.8)/40=k[/tex]
[tex]0.010984166494596147=k[/tex]
[tex]0.011=k[/tex]
Now that we have k=0.011, we can find the time (t) by which population will be 15 million:
[tex]A=A0*e^{k*t}[/tex]
[tex]15=5.8*e^{0.011t}[/tex]
[tex]ln(15/5.8)/0.011=t[/tex]
[tex]86.38111668634878=t[/tex]
[tex]86.38=t[/tex]
Because the starting year is 2000, and we need 86.38 years for increasing the population from 5.8 to 15 million, then by 2086 the population will be 15 million.
