anonymous
  • anonymous
Describe whether this is linear or nonlinear. Please explain. Photo attached.
Precalculus
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
DebbieG
  • DebbieG
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?
DebbieG
  • DebbieG
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.

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anonymous
  • anonymous
So this is not linear
DebbieG
  • DebbieG
correct. You see why, right?
DebbieG
  • DebbieG
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.
anonymous
  • anonymous
The slope ended up curving upwards.
anonymous
  • anonymous
I have one more, but it is worded. Can you help me? please @DebbieG
anonymous
  • anonymous
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?
DebbieG
  • DebbieG
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?
DebbieG
  • DebbieG
(and geeeez, you sure don't know how to keep a secret, huh?? ;) LOL
anonymous
  • anonymous
Non linear @DebbieG
DebbieG
  • DebbieG
Right. It's actually an exponential... \(\Large N(t)=2^{t+1}\)
anonymous
  • anonymous
@DebbieG whats actually an exponential?
DebbieG
  • DebbieG
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. :)

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