Question 3, 4.5.5
HW Score: $11.4\mathrm{\%},2.17$ of 19 points
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The exponential model $\mathrm{A}=745.1e^{0.008t}$ 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 $◻$
(Round to the nearest year as needed)

Step 1 ：The exponential model $A=745.1e^{0.008t}$ 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 $745.1\ast e^{0.008\ast t}=854$ for 't'.

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

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

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 $\boxed{{\displaystyle 2020}}$.