Question

the exponetial model A=354.7e^0.01t describes the population, A, of the country in milions, t years after 2003. Use the model to determined when the population of the country will be 438 million

Answer 1

The population of the country will be 438 million around 2011.

Step-by-step explanation:

The exponential model A=354.7e^(0.01t) represents the population, A, of a country in millions, t years after 2003. To determine when the population will be 438 million, we can substitute A=438 into the equation and solve for t:

438 = 354.7e^(0.01t)

Divide both sides by 354.7:

e^(0.01t) = 438/354.7

Take the natural logarithm of both sides to remove the base e:

ln(e^(0.01t))=ln(438/354.7)

0.01t=ln(438/354.7)

Divide both sides by 0.01 to isolate t:

t = ln(438/354.7)/0.01

Using a calculator, we can find that t is approximately 8.287 years after 2003. Therefore, the population of the country will be 438 million around 2011.