Problem

Complete the table shown to the right for the population growth model for a certain country.
\begin{tabular}{|c|c|c|}
\hline 2007 Population(millions) & Projected 2042 Population (millions) & Projected Growth Rate, $k$ \\
\hline 70.8 & & 0.0184 \\
\hline
\end{tabular}
The projected 2042 population is $\square$ million
(Round to one decimal place as needed)

Answer

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Answer

Final Answer: \(\boxed{134.8}\) million

Steps

Step 1 :Given the initial population (P0) in 2007 is 70.8 million, the growth rate (k) is 0.0184, and the time period (t) is the difference in years between 2042 and 2007, which is 35 years.

Step 2 :We can use the population growth model formula, which is represented as \(P = P_0e^{kt}\), where P is the final population, P0 is the initial population, k is the growth rate, and t is the time in years.

Step 3 :Substitute the given values into the formula to find P (2042 population).

Step 4 :\(P = 70.8e^{0.0184*35}\)

Step 5 :Calculate the above expression to get the projected 2042 population.

Step 6 :The projected 2042 population is approximately 134.8 million.

Step 7 :Final Answer: \(\boxed{134.8}\) million

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