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

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

@undeadknight26

Answer 2

@jim_thompson5910

Answer 3

First you'll need to calculate S(1) and S(4)

Answer 4

Right

Answer 5

what do you get for each?

Answer 6

I got it, let me type it up:

Answer 7

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

Answer 8

right idea, but the notation is off

Answer 9

The notation? Would you mind explaining a little more? :)

Answer 10

basically you're calculating the slope through (x1,y1) and (x2,y2)

where y1 = S(x1) and y2 = S(x2)

Answer 11

Ok

Answer 12

well you're not squaring y, it's y sub 2 (the 2 is below the y)

Answer 13

So, 1997 = S(4), 1993 = S(1)

Answer 14

not quite

Answer 15

you plug t = 1 into S(t) to find S(1)

Answer 16

OOOOooooohhhh!

Answer 17

So:

Answer 18

uuuuuhhhh.....could you please explain more please?

Answer 19

S(t) = t^2 + 5t + 52

S(1) = (1)^2 + 5(1) + 52 ... replace EVERY copy of t with 1

S(1) = ???

Answer 20

Oh poop, that's what I was going to put, but I was thinking of a different equation, hold on one sec, let me solve it! XD

Answer 21

\[S(1) = 1^2 + 5(1) + 52 = S(1) = 58?\]

Answer 22

good

Answer 23

S(4) = ??

Answer 24

Yeeeesssss...hehehe....let me solve that one...

Answer 25

\[S(4) = 4^2 + 5(4) + 52 = S(4) = 88\]

Answer 26

correct

Answer 27

OOOOOOOHHHHHHH.....I GOT IT. PLUG THOSE INTO THE AVERAGE RATE OF CHANGE RIGHT?

Answer 28

The formula?

Answer 29

exactly, visually the average rate of change is just the slope of the line through the two points

Answer 30

I understand now! I forgot the AROC is the slope! Ok, plug those into the parts in the formula and I'll get my answer, correct good sir?

Answer 31

that is correct

Answer 32

Alright, I'll answer it, hold on a sec.:

Answer 33

\[\frac{ 88 - 58 }{ 4 - 1 } = \frac{ 30 }{ 3 } = 10 million dollars!!!!!!\]

Answer 34

10 million is correct, but the units are dollars per yer

Answer 35

Mr. Thompson, would you mind deleting your answer about the "now use them to find the slope through (1,58) and (4,88) ?" I don't want other people to see how you got the answer, like just taking the answer without knowing what it means.

Answer 36

fair enough

Answer 37

Actually, I think others would benefit from seeing what jim wrote to you. He discusses a method, but does not provide an answer!

Answer 38

probably best to delete the whole question then (or at least that final answer) if you're concerned about that

Answer 39

Ok, I shall do that. @mathmale you are correct about that, but I know some students who just look at these questions, and take the answers. :(

Answer 40

Why? You will help other people?? :\

Answer 41

I know, but...I guess you're right.

Answer 42

I won't say the answer. How about that? :)

Answer 43

Your discussion with Jim has been a very good one. I see no harm done by leaving it posted as is.

Answer 44

Ok, I hope I didn't break any rules @mathmale

Answer 45

Relax. Not at all! On the contrary, you were a thoughtful participant in this discussion. What I'd give to see others participate as much as you have!

Why not go on to some new problems now? Good luck!

Answer 46

Taw, thank you for the kind words! I shall continue on my journey for new math problems to conquer. Farewell!