Question 3, 4.5.5 HW Score: $11.4 \%, 2.17$ of 19 points Points: 0 of 1 Save The exponential model $\mathrm{A}=745.1 e^{0.008 t}$ describes the population, $\mathrm{A}$, of a country in millions, $\mathrm{t}$ years after 2003 . Use the model to determine when the population of the country will be 854 million. The population of the country will be 854 million in $\square$ (Round to the nearest year as needed)

Step 1 ：The exponential model \(A=745.1 e^{0.008 t}\) describes the population, \(A\), of a country in millions, \(t\) years after 2003. We need to determine when the population of the country will be 854 million.

Step 2 ：We need to solve the equation \(745.1 * e^{0.008 * t} = 854\) for 't'.

Step 3 ：First, we divide both sides by 745.1 to isolate the exponential term, giving us \(e^{0.008 * t} = \frac{854}{745.1}\).

Step 4 ：Next, we take the natural logarithm of both sides to solve for 't', giving us \(0.008 * t = ln\left(\frac{854}{745.1}\right)\).

Step 5 ：Finally, we divide both sides by 0.008 to solve for 't', giving us \(t = \frac{ln\left(\frac{854}{745.1}\right)}{0.008}\).

Step 6 ：Calculating the right side of the equation gives us \(t = 17\). This means the population of the country will be 854 million 17 years after 2003.

Step 7 ：Final Answer: The population of the country will be 854 million in \(\boxed{2020}\).