Explanation:
Here we know that the linearized regression equation for an exponential data set is:
[tex]log \hat{y} = 0.14x + 0.4[/tex]
Where:
[tex]\text{x: The number of years and} \\ \\ \text{y: The population}[/tex]
The predicted population when [tex]x=5[/tex] is found by substituting this value into the equation and finding [tex]y[/tex]:
[tex]log \hat{y} = 0.14x + 0.4 \\ \\ log \hat{y} = 0.14(15) + 0.4 \\ \\ log \hat{y} = 2.5 \\ \\ \hat{y}=10^{2.5} \\ \\ \hat{y} \approx 316.227[/tex]
Since population is a natural number, we must round off, therefore, the predicted population is 316, option C.
