Question

The table below represents the displacement of a turtle from its nest as a function of time:

Time
(hours)
x Displacement
from nest
(miles)
y
0 5
1 27
2 49
3 71
4 93


Part A: What is the y-intercept of the function, and what does this 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

I NEED HELP PLEASE ????????? HELP MEEEEEE

Answer 2

`Part A: What is the y-intercept of the function, and what does this tell you about the turtle?`

when x = 0, what is the value of y?

Answer 3

The information is given in the table

Answer 4

yea

Answer 5

do you see where I'm referring to?

Answer 6

no sorry not that good at math

Answer 7

look at the row that has x = 0
what is next to that value?

Answer 8

5

Answer 9

so x = 0 and y = 5 pair up

giving the ordered pair (0,5)

Answer 10

what this means is that at time 0 hours, the distance is 5 miles

basically the turtle is 5 miles away from the nest at the beginning

Answer 11

ok so i write a equation

Answer 12

no you just use words to explain what the y intercept means

Answer 13

similar to how I explained it just now

Answer 14

ok got it .......................so for part B I din't know how to do it can you help me

Answer 15

`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.`

fill in these blanks

if x = 1, then y = ________
if x = 4, then y = ________

Answer 16

Y=27
Y=93

Answer 17

so we have these two points that are of interest to us

(1,27) and (4,93)

Answer 18

find the slope through those two points to get the answer

Answer 19

slope formula

\[\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]

Answer 20

if thats not right then i think it might be m=-66/3

Answer 21

you should get 66/3 which reduces to 22

Answer 22

yep

Answer 23

what does this mean in terms of the problem?

Answer 24

22 miles i think

Answer 25

close

Answer 26

not quite the full picture though

Answer 27

slope = 22 = 22/1

this means that each time x increases by 1, y increases by 22

each time the hour amount goes up by 1, the mile amount goes up by 22

basically the turtle is going (22 miles)/(1 hour) = 22 mph. This is a very fast turtle lol

Answer 28

yea lol thanks