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: 1000 1050 1102.50 1,157.63 1215.51
Did the number of people at Jacob's store increase linearly or exponentially? (4 points)


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 1

@vishweshshrimali5

Answer 2

To see whether the increase is linear or exponential... Do one thing.. calculate the slope between two consecutive points...

Slope = Change in sale/ Change in number of months

Answer 3

Can you do this?

Answer 4

Does that mean I have to find the percentage increase?

Answer 5

No .. percentage is not required... Just relative change

Answer 6

Then no I don't know how to do this

Answer 7

Okay let me show you for one set of points...

Month: 1 2
Sale: 1000 1050

Now, change in sale = 1050 - 1000 = 50
Change in number of months = 2 - 1 = 5

Slope = 50 / 5 = 10

Answer 8

Can you do this for rest of the points?

Answer 9

Sure but it'll take a few minutes

Answer 10

Find the slope between, ( 2 and 3), (3 and 4), (4 and 5)

Answer 11

Wait I just have a question... Why is the change in the number of months 5?

Answer 12

Hmm? Between month 4 and month 5 you mean?

Answer 13

no between 1 and 2

Answer 14

Ohh sorry that's my mistake :)

Answer 15

That should be change in number of months = 1

Slope = 50 / 1 = 50

Answer 16

ok thanks

Answer 17

now i'll just continue doing the rest

Answer 18

Sure

Answer 19

ok so for months 2 and 3 the slope = 52.5
3 and 4 the slope = 55.3
4 and 5 the slope = 57.88

Answer 20

Great!

So, you see that the relative change (and thus percentage change) is not constant so the change is exponential

Answer 21

One more question before moving on. It's something that always confuses me. What is the difference between linear, or constant, and exponential?

Answer 22

Sorry if that's a dumb question. I'm just not that good at math.

Answer 23

Actually, linear change means that the changes are increasing is with equal amount...
Constant means that changes are same
Exponential means that difference between changes is increasing in a non-equal amount ...

Answer 24

Oh. Thanks for explaining. Can I just have like 2 minutes to quickly write this down?

Answer 25

Sure! Take your time :)

Answer 26

ok thanks i'm done!

Answer 27

@vishweshshrimali5

Answer 28

So, @Fairy733189 you want to ask anything?

Answer 29

no I actually figure it out and I understand it now but can you help me on another problem