Question

The exponential model A - 19.40.0171 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 28 million

DOO
The population of the country will be 28 million in
(Round to the nearest year as needed.)

Answer 1

The population of the country will be 28 million in the year 2140.

Step-by-step explanation:

To determine when the population of the country will be 28 million, we can set up the exponential equation:

A = 19.40(0.0171)^t

Where A represents the population in millions, t represents the number of years after 2003, and 0.0171 is the growth factor.

We want to find the value of t when A is 28 million:

28 = 19.40(0.0171)^t

Divide both sides of the equation by 19.40 to isolate the exponential term:

1.4433 = (0.0171)^t

To solve for t, we need to take the logarithm base 0.0171 of both sides:

t = log0.0171(1.4433)

Using a calculator, we find that t is approximately 136.5 years after 2003. Rounded to the nearest year, the population of the country will be 28 million in the year 2140.