Question

he exponential model Upper A equals 347.5 e Superscript 0.024 t describes the​ population, A, of a country in​ millions, t years after 2003. Use the model to determine when the population of the country will be 510 million.

Answer 1

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.

$P(t) = 347.5e^{0.024t}$

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

$P(t) = 347.5e^{0.024t}$

$510 = 347.5e^{0.024t}$

$e^{0.025t} = \frac{510}{347.5}$

Applying ln to both sides, so we can find t

$\ln{e^{0.025t}} = \ln{\frac{510}{347.5}}$

$t = \frac{\ln{\frac{510}{347.5}}}{0.025}$

$t = 15.35$

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.