Respuesta :
Answer:
The population of the country will be 510 million during the year of 2018.
Step-by-step explanation:
The exponential model for the population, in millions, t years after 2003 is.
[tex]P(t) = 347.5e^{0.024t}[/tex]
Use the model to determine when the population of the country will be 510 million.
t years after 2003, in which t is found when P(t) = 510. So
[tex]P(t) = 347.5e^{0.024t}[/tex]
[tex]510 = 347.5e^{0.024t}[/tex]
[tex]e^{0.025t} = \frac{510}{347.5}[/tex]
Applying ln to both sides, so we can find t
[tex]\ln{e^{0.025t}} = \ln{\frac{510}{347.5}}[/tex]
[tex]t = \frac{\ln{\frac{510}{347.5}}}{0.025}[/tex]
[tex]t = 15.35[/tex]
15.35 years after 2003, so during the year of 2018.
The population of the country will be 510 million during the year of 2018.
