Answer:
The average rate of change is equal to [tex]\frac{3}{4}\frac{homeruns}{game}[/tex]
Step-by-step explanation:
we have
[tex]n(x)=\frac{3}{4}x[/tex] -----> this is a linear direct variation
we know that
The rate of change of a linear variation is a constant
The rate of change of a linear variation is equal to the slope of the line
In this problem the slope of the line is equal to [tex]m=\frac{3}{4}\frac{homeruns}{game}[/tex]
therefore
The average rate of change is equal to [tex]\frac{3}{4}\frac{homeruns}{game}[/tex]
Verify
the average rate of change is equal to
[tex]\frac{n(b)-n(a)}{b-a}[/tex]
In this problem we have
[tex]n(a)=n(12)=\frac{3}{4}(12)=9\ homeruns[/tex]
[tex]n(b)=n(60)=\frac{3}{4}(60)=45\ homeruns[/tex]
[tex]a=12\ games[/tex]
[tex]b=60\ games[/tex]
Substitute
[tex]\frac{45-9}{60-12}=\frac{3}{4}\frac{homeruns}{game}[/tex]
