Question

Describe whether this is linear or nonlinear. Please explain.
Photo attached.

Answer 1

If it is linear, then the ratio of the change in x's to the change in y's is a constant (slope).

That is, if the change in y from x=0 to x=2 is 5 units, then the change in y from x=2 to x=4 is also 5 units, and so on, for any change in x of 2 units the change is y is the same.

Is that true here?

Answer 2

Also, you could plot those points and look at it to see if it appears to be a straight line. That is not enough to PROVE that it is or isn't, but it will give you some intuition about whether it is or it isnt.

Answer 3

So this is not linear

Answer 4

correct. You see why, right?

Answer 5

Another way to tell is, if you took 2 of those points and compute slope, and then took a different 2 of the points and computed slope, the slopes would not be the same. For a linear equation, the slope is constant.

Answer 6

The slope ended up curving upwards.

Answer 7

I have one more, but it is worded. Can you help me? please @DebbieG

Answer 8

You have a secret that you tell one person. Every hour, each of the people that know the secret tells one person. The number of people who know is N, and t is the number of hours since you told the first person. Is N a linear function of t?

Answer 9

So let's think about what's happening here. We can actually come up with some points on the function N(t).

You tell one person, and an hour later, "each of the people that knows the secret" tells one person. So that means after one hour, you and the person you told have each told someone. So at time t=1, 4 people know.

N(1)=4

An hour later, each of them tells another person, so now 8 people know:
N(2)=8

An hour later, each of them tells another person:
N(3)=16

An hour later, each of them tells another person:
N(4)=32

So there are some points on this function:

(1,4) (2,8) (3,16) (4,32)

And so on.

Now apply what we talked about above and tell me: linear? or not?

Answer 10

(and geeeez, you sure don't know how to keep a secret, huh?? ;) LOL

Answer 11

Non linear @DebbieG

Answer 12

Right. It's actually an exponential... \(\Large N(t)=2^{t+1}\)

Answer 13

@DebbieG whats actually an exponential?

Answer 14

Sorry, the function N(t) is. But don't worry about that, you don't need to know that to answer the question. Didn't mean to cause confusion. :)