Question

PLEASE HELP!!

The exponential model A=308e^0.026t 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 655 million.
The population of the country will be 655 million in what year

Answer 1

Answer: In 2042 the population of the country will be 655 million.

Explanation:

Given: The exponential model
`A=308e^(0.026t)` describes the​ population, A, of a country in​ millions, t years after 2003.

When population of the country will be 655 million. we have

`655=308e^(0.026t)\\\\\Rightarrow\ (655)/(308)=e^(0.026t)\\\\\Rightarrow2.1266 =e^(0.026t)`

Taking natural log on both sides

`\ln 2.1266 =\ln e^(0.026t)\\\\\Rightarrow\ 0.754524460235=0.026t\\\\\Rightarrow\ t=(0.754524460235)/(0.026)=29.0201\approx29`

Hence, in 2042 the population of the country will be 655 million. [2013+29 = 2042]