Respuesta :
Answer:
The prediction for the population in 2012 will be of 324.9 million.
Step-by-step explanation:
Exponential equation for population growth:
Considering that the population growth varies directly with time, it's value after t years is given by:
[tex]P(t) = P(0)e^{kt}[/tex]
In which P(0) is the initial value and k is the growth rate.
The population of the United States in 1990 was approximately 249 million
This means that [tex]P(0) = 249[/tex], so:
[tex]P(t) = P(0)e^{kt}[/tex]
[tex]P(t) = 249e^{kt}[/tex]
In 2000, 281 million.
2000 - 1990 = 10, so [tex]P(10) = 281[/tex]. We use this to find k.
[tex]P(t) = 249e^{kt}[/tex]
[tex]281 = 249e^{10k}[/tex]
[tex]e^{10k} = \frac{281}{249}[/tex]
[tex]\ln{e^{10k}} = \ln{\frac{281}{249}}[/tex]
[tex]10k = \ln{\frac{281}{249}}[/tex]
[tex]k = \frac{\ln{\frac{281}{249}}}{10}[/tex]
[tex]k = 0.0121[/tex]
So
[tex]P(t) = 249e^{0.0121t}[/tex]
Use this information to predict the population for 2012.
2012 - 1990 = 22, so this is P(22).
[tex]P(22) = 249e^{0.0121*22} = 324.9[/tex]
The prediction for the population in 2012 will be of 324.9 million.
