Question

the table below represents the displacement of a turtle from its nest as a function of time.Part A. What is the y intercept of the function and what does it tell you about the turtle?part b. calculate the average rate of change of the function represented by the table between x = 1 to x = 4 hours and tell what the average rate represents.part c. what would be the domain of the function if the turtle continued to walk at this rate until it traveled 225 miles from the nest?

Answer 1

Part A.

Y intercept is the coordinate (0,y), when the function has an x value of 0, it is the y intercept.

In this case:

(0,5) =

y intercept = 5

IT tells about the turtle that it starts at a nest displacement of 5 miles.

Part B

The average rate of change represents the speed .

x1=1 ,y1=27

x2=4 ,y2=93

We have to calculate the slope if the function:

$\text{slope}=\text{ }\frac{y2-y1}{x2-x1}$

Replace:

$\text{slope}=\frac{93-27}{4-1}\text{ = }\frac{66}{3}=22$

Part C.

speed = distance /time

time= distance / speed

time= 225 / 22 = 10.22 hours

The domain will be

0< x ≤ 10.22