Question

The table below shows the sale, in dollars, at Jacob's store over a period of five months:


Month
1
2
3
4
5
Sale
1,000
1,050
1,102.50
1,157.63
1,215.51


Did the number of people at Jacob's store increase linearly or exponentially?

Answer 1

Linearly, because the table shows a constant percentage increase in sales per month

Exponentially, because the table shows a constant percentage increase in sales per month

Linearly, because the table shows that sales increase by an equal factor for an equal increase in months

Exponentially, because the table shows an equal increase in sales for an equal increase in months

Answer 2

notice the change from 1000 to 1050 is +50

since 1050-1000 = 50

Answer 3

then when we go from 1050 to 1,102.50 we have increased by 52.5


Scratch Work: 1102.50 - 1050 = 52.5

Answer 4

So because the increase of +50 and the increase of +52.5 are NOT the same, this means we do NOT have a linear function

The increases need to be the same each time

Answer 5

oh ok my guess is that it is the second one. am i right?

Answer 6

you are correct

Answer 7

thank you very much you the BEST!

Answer 8

it looks like it is increasing by 5% each time

5% of 1,000 = 50 ---> increase of 50

5% of 1050 = 52.5 ---> increase of 52.5

etc etc

so that further reinforces the idea that this function is exponential

Answer 9

np

Answer 10

yep i got it i just wasnt really sure

Answer 11

could you help with one more if u can?

Answer 12

sure

Answer 13

The functions f(x) and g(x) are described using the following equation and table:

f(x) = -3(1.02)x


x g(x)
-1 -5
0 -3
1 -1
2 1


Which statement best compares the y-intercepts of f(x) and g(x)?
The y-intercept of f(x) is equal to the y-intercept of g(x).

The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).

The y-intercept of g(x) is equal to 2 times the y-intercept of f(x).

The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).

Answer 14

My answer is the first one am i right?

Answer 15

I'm assuming you're dealing with

\[\Large f(x) = -3(1.02)^x\]

right?

Answer 16

yeah

Answer 17

what happens when x = 0 for f(x)?

Answer 18

it equals -3

Answer 19

So f(0) = -3

Answer 20

what is g(0) equal to

Answer 21

also -3

Answer 22

that tells us the y-intercepts for each f(x) and g(x) are both -3

Answer 23

ok again thank you you the BEST! :D :D :D :D

Answer 24

sure thing

Answer 25

thats it thats all i need :D

Answer 26

Thank You