Question

The n number of homeruns hit during the regular season by a certain baseball player can be modeled by the function n(x) =3/4x, where x is the number of games that have been played. Find the average rate of change from game 12 to game 60.

Answer 1

Answer:

The average rate of change is equal to $\frac{3}{4}\frac{homeruns}{game}$

Step-by-step explanation:

we have

$n(x)=\frac{3}{4}x$ -----> 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 $m=\frac{3}{4}\frac{homeruns}{game}$

therefore

The average rate of change is equal to $\frac{3}{4}\frac{homeruns}{game}$

Verify

the average rate of change is equal to

$\frac{n(b)-n(a)}{b-a}$

In this problem we have

$n(a)=n(12)=\frac{3}{4}(12)=9\ homeruns$  

$n(b)=n(60)=\frac{3}{4}(60)=45\ homeruns$  

$a=12\ games$

$b=60\ games$

Substitute

$\frac{45-9}{60-12}=\frac{3}{4}\frac{homeruns}{game}$