Question

The exponential models describe the population of the indicated country, A, in millions, t years after 2006. By what percentage is the population of that country increasing each year? A. Country 4. A= 25.8e^0.021t has the greatest growth. B. The population of that country is increasing by __% each year. (Round to the nearest tenth as needed)

Answer 1

The population of that country is increasing by 2.1% each year.

Explanation:

The exponential model of the population on the greatest growth:

`A=25.8e^(0.021t)`

To determine at what percentage is the population increasing each year, we can use the following ratio:

`(A(t+1))/(A(t))`

Therefore,

`(A(t+1))/(A(t))=(25.8e^(0.021(t+1)))/(25.8e^(0.021t))=e^(0.021)=1.021\text{ }`

The population of that country is increasing by 2.1% each year.