Question

Linda is studying the sale of a particular brand of cereals from the year 1993 to 2004. She writes the following function to model the sale of the cereal S(t), in million dollars, after t years:

S(t) = t2 + 5t + 52

Part A: What does the y-intercept of the graph of the function represent? (4 points)

Part B: What is the reasonable domain of the graph of the function? (3 points)

Part C: What is the average rate of change of the sale of the cereal from the first year to the fourth year? Show your work. (3 points)

Answer 1

ok so for this one i graphed it and i see that the y intercept is 0,52 but im not sure what it represents

Answer 2

ill post what the graph looks like

Answer 3

what do you think pawtpie

Answer 4

hmm

Answer 5

The y intercept would have to be the value when t = 0

Answer 6

i understand that but i have no idea what it would represent maybe the starting price

Answer 7

@Pawtpie so when t=0 should be how much cereal she starts with I would think

Answer 8

i mean the starting amount of cereal

Answer 9

I think that would be the starting amount of 52 in millions

Answer 10

oh ok

Answer 11

and for the domain i know that the domain is all real numbers am i right

Answer 12

@melancholymushroom yes

Answer 13

ok so i would have to come up with something like this x<?<y right

Answer 14

I think so yes

Answer 15

ok so how exactly do i do this do i take all the x values

Answer 16

Maybe the x value increases by 1 each year so it would be the difference in years.

Answer 17

so 1 less than or equal x ? somthing like that

Answer 18

Well if we're looking at the years between 1993 and 2004 that's 11 years

Answer 19

so maybe it's 0<x<11

Answer 20

ok

Answer 21

hold on small typo actually

Answer 22

the problem is that i need it to be more than or equal too but how do i write that out on my keyboard

Answer 23

actually might be 0<=x<=11

Answer 24

I think we would just write the domain as {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} instead

Answer 25

ok and for part c i do average rate of change so that would be is it years/amount of change

Answer 26

x-y/x-y

Answer 27

is the bottom supposed to be the years or the difference in numbers

Answer 28

Maybe we just use the formula for the slope between two points is what you're saying

Answer 29

hold on

Answer 30

I guess we just get S(1) and S(4) for t to get the 2 ordered pairs and then get the slope

Answer 31

for the average rate of change i know its supposed to be the difference in the amount of year so 4-1 and the difference in teh amount of cereal sold which was 88-?

Answer 32

im trying to find the second point

Answer 33

All I did to get the points was find S(1) and S(4)

Answer 34

ok then i guess im doing it wrong what do i do to find the average rate of change

Answer 35

cuz i have to find the average rate of change from year 4 to 1

Answer 36

Ok first we need 2 ordered pairs to find the slope from them

Answer 37

What I did was I got S(1) and S(4)

Answer 38

ok two points were 1,58 and 4,88

Answer 39

I got (4, 78) for the second one

Answer 40

oh whoops i meant 78 typo

Answer 41

Ok so it seems that all we have to do is find the distance between the two points:

\[Slope = \frac{ rise }{ run }=\frac{ y2 - y1 }{ x2 - x1 }\]

Answer 42

For (1, 58) and (4, 78)

Answer 43

so would it be 1/10 or 10/1

Answer 44

I'll check real quick

Answer 45

k

Answer 46

Seems I got 20/3

Answer 47

\[\frac{ 78 - 58 }{ 4 - 1 } = \frac{ 20 }{ 3 }\]

Answer 48

oh whoops i put 88 instead of 78 i see now

Answer 49

alright thats pretty much it thanks for all the help i really appreciate it

Answer 50

No problemo :)

Answer 51

btw nice profile pic lol what is it

Answer 52

Honestly have no idea, I just choose from the Google images of "derp".

Answer 53

lol good to know thanks for all the help

Answer 54

:3

Answer 55

No problem again lol