Respuesta :
Answer:
The population in 2011 will be of 34.88 million people.
Step-by-step explanation:
The population after t years is modeled by an exponential function is the following format:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the growth rate.
At the beginning of 1990, 21.7 million people lived in the metropolitan area of a particular city.
This means that [tex]P(0) = 21.7[/tex]
The 1998 population was 26 million.
1998 is 8 years after 1990. So [tex]P(8) = 26[/tex]
We use this to find the value of r.
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]26 = 21.7e^{8r}[/tex]
[tex]e^{8r} = \frac{26}{21.7}[/tex]
[tex]\ln{e^{8r}} = \ln{\frac{26}{21.7}}[/tex]
[tex]8r = \ln{\frac{26}{21.7}}[/tex]
[tex]r = \frac{\ln{\frac{26}{21.7}}}{8}[/tex]
[tex]r = 0.0226[/tex]
So
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]P(t) = 21.7e^{0.0226t}[/tex]
If this trend continues, how large will the population be in the year 2011?
2011 is 21 years after 1990. So this is P(21).
[tex]P(t) = 21.7e^{0.0226t}[/tex]
[tex]P(21) = 21.7e^{0.0226*21}[/tex]
[tex]P(21) = 34.88[/tex]
The population in 2011 will be of 34.88 million people.
