Question

I'm literally about to cry from this problem, medal and fan will be rewarded for help. :(

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) = t^2 + 5t + 52

Part A: What does the y-intercept of the graph of the function represent?

Part B: What is the reasonable domain of the graph of the function?

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.

Answer 1

do you mean t^2?

Answer 2

Yeah, I should edit that. :)

Answer 3

\[S(t) = t^2 + 5t + 52\]right?

Answer 4

Correct @satellite73

Answer 5

Is Part A y is zero?

Answer 6

oh no

Answer 7

Ok, I think it's 52, for sure.

Answer 8

part A is asking for the domain of the function

Answer 9

Oh!

Answer 10

oops that is part B

Answer 11

Haha, it's cool. XD I think y-intercept is 52.

Answer 12

A is y intercept, which is what you get if \(t=0\) namely \(52\)

Answer 13

So, Part A is 52? :)

Answer 14

i thought part A would be the year 1993 but I'm not sure :/

Answer 15

yes, and it means that in 1993 they solve $52 million

Answer 16

Oh! Ok, would you mind helping me with Part B and C? I understand Part A. now :-)

Answer 17

sure
the question is a little fuzzy
i suppose it to mean that it is \(S(t) = t^2 + 5t + 52\) where we start counting time in \(1993\)

Answer 18

Is this for Part B.?

Answer 19

and stop in \(2004\)
since \(2004-1993=11\) i would say the domain is \(0\leq t\leq 11\)

Answer 20

that would be part B yes

Answer 21

unless i am reading it wrong and you are supposed to use \(1993\leq t\leq 2004\)
but that doesn't make any sense for the first problem, so lets go with the first answer

Answer 22

Domain for Part B. is \[0 \le t \le 11\]

Answer 23

Ok, may I ask why the 11 is here? :)

Answer 24

because it is eleven years from 1993 to 2004

Answer 25

OOOOoohhhhh duuuurrrr!!! Brain fart, haha, ok. XD

Answer 26

I understand, so the first one with the eleven is more reasonable as an answer than the 1993 is less than or equal to, etc. etc. ?

Answer 27

i think so, yes
the question is not written very well

Answer 28

I know, I completely understand.

Answer 29

What about part C.? Would you mind explaining to me about that one?

Answer 30

Good morrow sir @halorazer

Answer 31

Oh! Hold on!

Answer 32

again it is not written very well
is the first year
\(t=1\) or is it \(1993\) which would make \(t=0\)?

Answer 33

\[\frac{ y^2 - y^1 }{ x^2 - x^1 }\]

Answer 34

right?

Answer 35

i would say \(t=0\) and \(t=3\) i.e. 1993 and 1997

Answer 36

yes right

Answer 37

It would look like this:

Answer 38

i meant \(t=4\)but you have the right idea

Answer 39

oops

Answer 40

Wait, hold on.

Answer 41

\[\frac{s(4)-s(0)}{4}\]

Answer 42

\[\frac{ 1997 - 1993 }{ 4 - 1 } = \frac{ 4 }{ 3 } = 1.33333...\]

Answer 43

@Indigo

Answer 44

@satellite73

Answer 45

@satellite73 help!

Answer 46

@satellite73

Answer 47

@amistre64

Answer 48

@satellite73

Answer 49

@satellite73 please don't leave!!!

Answer 50

@satellite73 I still need help!