Option C: [tex]316[/tex] is the predicted population when [tex]x=15[/tex]
Explanation:
The regression equation for an exponential data is [tex]\log y=0.14x+0.4[/tex]
Where x is the number of years and
y is the population
We need to determine the predicted population when [tex]x=15[/tex]
The population x can be determined by substituting [tex]x=15[/tex] in the equation [tex]\log y=0.14x+0.4[/tex]
Thus, we have,
[tex]\log y=0.14(15)+0.4[/tex]
[tex]\log y=2.1+0.4[/tex]
[tex]\log y=2.5[/tex]
Using the logarithmic definition [tex]\log _{a}(b)=c[/tex] then [tex]b=a^{c}[/tex]
[tex]\log _{10}(y)=2.5 \Rightarrow y=10^{2.5}[/tex]
[tex]y=316.22776 \ldots[/tex]
Rounding off to the nearest whole number, we get,
[tex]y=316[/tex]
Thus, the predicted population when [tex]x=15[/tex] is 316
Hence, Option C is the correct answer.
