Answer :
Since we know that a varies directry with b, this means that
[tex]\frac{a}{b}=k[/tex]where k is a proportional constant.
If we plugg in the values we have we can find k. Then
[tex]\begin{gathered} k=\frac{8}{20} \\ =\frac{2}{5} \end{gathered}[/tex]Therefore, in our case
[tex]\frac{a}{b}=\frac{2}{5}[/tex]Now we want to know the value of a when b=14.5, plugging the value in the last equation we have
[tex]\frac{a}{14.5}=\frac{2}{5}[/tex]Now we solve for a
[tex]\begin{gathered} \frac{a}{14.5}=\frac{2}{5} \\ a=\frac{2}{5}\cdot14.5 \\ a=2.8 \end{gathered}[/tex]Therefore, when b=14.5 than a=2.8.