Question

PLEASE HELP!!!!!!!!!!

Kim is studying the sale of a particular brand of cereals from the year 2000 to 2010. She writes the following function to model the sale of the cereal S(t), in million dollars, after t years:

S(t) = t^2 + 7t + 69

What is the reasonable domain of the graph of the function?

Answer 1

@kropot72 @jim_thompson5910 @satellite73

Answer 2

domain refers to the set of allowed inputs of a function

Answer 3

what is the input variable?

Answer 4

t?

Answer 5

t represents what?

Answer 6

the years right?

Answer 7

yes t is time in years

so t = 0 represents 0 years (aka the starting point)

t = 1 is year 1
t = 2 is year 2
etc etc

Answer 8

so can I reasonably say t = -2 and plug this into the function?

Answer 9

no :) there is no such thing as negative time

Answer 10

so t has to be 0 or positive

Answer 11

it also states that the range is from "2000 to 2010"

so like most mathematical models, this is limited to a very specific timeframe

Answer 12

so this model wouldn't make much sense if we extended it out to say 2030 (it could be way off)

Answer 13

so the domain is 0 ≤ x ≤ 2010?

Answer 14

?

Answer 15

t is used instead of x

Answer 16

t is the time in years

if you're starting at the year 2000, then t = 0 represents the year 2000

t = 1 represents 2001
t = 2 for 2002
t = 3 for 2003

etc etc

it's a short hand way to write it

Answer 17

we can only go to 2010 because anything beyond that could mean the model is off

Answer 18

so the largest domain possible is

\[\Large 0 \le t \le 10\]

now that I think about it, I guess you could extrapolate into the future a bit (maybe at most 10 years), but be careful not to go too far

Answer 19

Thank you! :)
Do you think u could help with 1 more?

Answer 20

sure

Answer 21

Okay thanks :)

What does the y-intercept of the graph of the function represent (using the same function as before)

Answer 22

the y intercept is when x = 0

in this case, t is used instead of x

so its when t = 0

Answer 23

t = 0 is the starting point

we start at the year 2000

so it represents the sales at the starting year 2000

Answer 24

plug in t = 0 and you get ???

Answer 25

69 ?

Answer 26

correct, so the sales in the year 2000 are $69 million

Answer 27

wait, so what does it represent?

Answer 28

scroll back up and re-read what I posted above

Answer 29

oh, the starting point. so i write, it represents $69 million in sales of the cereal at the beginning of her study?

Answer 30

which is the year 2000, yes

Answer 31

thank you so much :) <3 :-*

Answer 32

you're welcome