Question

a local newspaper charges by the number of words for advertising. write a function to represent the advertising costs
10 words:7.50, 15 words:8.75
20 words:10.00, 25 words:11.25

Answer 1

hint: what do you think your independent and dependent variables are?

Answer 2

is this still for the Arithmetic sequence?

Answer 3

well I guess you could treat this as a sequence but you would probably want to write it as a function instead

Answer 4

like f(x) = __________

Answer 5

then i wouldn't know
I'm still in middle school and i just started this unit

Answer 6

when we have one "variable" (in this case, the number of words) that determines the other (the price), we can write "function" which is a rule that tells us what the value of the independent variable is, if we input a certain dependent variable

Answer 7

(I realize that is kind of confusing so let me give an example)

Answer 8

Let's say a store is selling candy for 10 cents a piece. There are two things that are "varying" here; the number of candies, and the total amount paid.

Answer 9

Just using basic arithmetic (multiplication) we can determine the money paid simply by multiplying the price per candy by the number of candies

so 1 candy --> 0.10 * 1 = $0.10 or 10 cents
2 candy -- > 0.1 * 2 = $0.20 or 20 cents

Answer 10

now, we want to figure out a "function" which will tell us the price paid for a generic number of candies, x

Answer 11

oooohhh
i get it

Answer 12

we can say:

price = 0.10 * number of candies

or, in more "mathematical" terms

f(x) = 0.10x

make sense so far?

Answer 13

yes

Answer 14

so if we let x = 1 candy we get

f(1) = 0.10*1 = $0.10 which is the same as our manual calculations from earlier

Answer 15

yes

Answer 16

Now, your problem is a bit more difficult but the same principle applies

Answer 17

so this is what i got so far
a(n)=5.25+(n-1)0.25

Answer 18

i think this is right but not 100% sure

Answer 19

If your teacher wants you to use series/sequence notation, then sure, we can go with that

Answer 20

how would you do it?

Answer 21

yeah, your math looks right to me, good job ^^

Answer 22

hm

Answer 23

Doing the math I end up with f(x) = 5 + 0.25x

But if you haven't started learning function notation, then go with your original answer.

Answer 24

i did but i learned it this way too

Answer 25

but I'm wondering if there is a more easier way to do these kind of problems

Answer 26

have you learned anything about slope-intercept form yet?

Answer 27

yes

Answer 28

if you treat:

10 words:7.50, 15 words:8.75

as two points (10,7.50) and (15,8.75) you can just calculate the slope and y-intercept between them

Answer 29

i see

Answer 30

so using our slope formula m = (y2-y1)/(x2-x1) we get

(8.75-7.50)/(15-10) = 0.25

Answer 31

yes

Answer 32

and then you just substitute that m into f(x) = mx + b to get your y-intercept

Answer 33

oh

Answer 34

(keep in mind this only works for linear equations - or sequences with a common difference)

Answer 35

ok. thank you so much!

Answer 36

np