Question

What is the rate of change for the function on the table? 15 grapes eaten per minute 15 minutes to eat each grape 60 grapes eaten per minute 60 minutes to eat each grape

Answer 1

Solution:

Rate of change = Slope between two points

Rate of change of two points is given by=$\frac{dy}{dx}= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Rate of change of  15 grapes eaten per minute 15 minutes to eat each grape 60 grapes eaten per minute 60 minutes to eat each grape

       =$\frac{60-15}{60-15}=\frac{45}{45}=1$

Answer 2

Answer:

$rate\ of\ change\ of\ a\ function$ = 15.

Step-by-step explanation:

Given :  15 grapes eaten per minute 15 minutes to eat each grape 60 grapes eaten per minute 60 minutes to eat each grape.

To find : What is the rate of change for the function on the table.

Solution : We know that rate of change of a function can be found by vertical change of the function divided by horizontal change of the function.  

Rate of change of a function =

$\frac{vertical\ change}{horizontal\ change}$

Rate of change of a function :

$\frac{y_{2} -y_{1}}{x_{2} -x_{1}}$.

$y_{2} -y_{1}$ = Difference between two y-coordinates.

$x_{2} -x_{1}$ =Difference between two x-coordinates.

$rate\ of\ change\ of\ a\ function$ =

$\frac {60-15}{4-1}$.

$rate\ of\ change\ of\ a\ function$ =$\frac {45}{3}$.

$rate\ of\ change\ of\ a\ function$ = 15.

Therefore, $rate\ of\ change\ of\ a\ function$ = 15.