Question

The exponential model A=792.2e^0.029t describes the population, A, of a country in millions, two years after 2003.

Use the model to determine when the population of the country will be 1122 million

Answer 1

To determine when the population of the country will reach 1122 million, we can use the given exponential model A = 792.2e^(0.029t), where A represents the population in millions and t represents the number of years after 2003.

Let's substitute A with 1122 and solve for t:

1122 = 792.2e^(0.029t)

To isolate e^(0.029t), we divide both sides by 792.2:

1122/792.2 = e^(0.029t)

1.416 = e^(0.029t)

To solve for t, we need to take the natural logarithm (ln) of both sides:

ln(1.416) = ln(e^(0.029t))

Using the property of logarithms that ln(e^x) = x, we simplify further:

ln(1.416) = 0.029t

Now, we can solve for t by dividing both sides by 0.029:

t = ln(1.416)/0.029

Using a calculator, we find that ln(1.416) ≈ 0.3466.

Substituting this value into the equation, we get:

t ≈ 0.3466/0.029

Simplifying further, we find:

t ≈ 11.95

Therefore, according to the exponential model, the population of the country will reach 1122 million approximately 11.95 years after 2003.

Explanation: