Chapter 12, Problem T12.10SPT

To determine

To find out which of the following is the best estimate for the population of the country in the year $2020$ , based on this equation.

Answer to Problem T12.10SPT

Option (c) is the correct option.

Explanation of Solution

A scatterplot reveals a clear curved relationship between population and year. However, a different scatterplot reveals a strong linear relationship between the logarithm of the population and the year. The given linear regression line is:

  $\ln (\text{<mover accent="true"><mo>p</mo><mo>^</mo></mover> opulation)}=-13.5+0.01(\text{Year})$

Now, we will replace the year by $2020$ , then it will be:

  $\begin{array}{l}\ln (\text{<mover accent="true"><mo>p</mo><mo>^</mo></mover> opulation)}=-13.5+0.01(\text{Year})\\ \Rightarrow \ln (\text{<mover accent="true"><mo>p</mo><mo>^</mo></mover> opulation)}=-13.5+0.01(\text{2020})\\ =6.7\\ \text{Take the exponential of each side:}\\ \text{Population}={10}^{6.7}\\ =5011872\\ \approx 5000000\end{array}$

Thus, option (c) is the correct option.