About this video
Jordan adopts cats at a constant rate, and a graph shows her number of cats C against days since moving, T. Sal reads the starting value at T = 0 (10 cats) and uses the point (15, 40) to find the rate: a change of 30 cats over 15 days is 2 cats per day. He then rules out the other answer choices.
You'll be able to
- read the starting value of a linear graph at time 0.
- find a rate of change using change in C over change in T.
- check statements about a linear situation against a graph.
Key words
- constant rate
- Changing by the same amount each unit of time, like 2 cats every day.
- delta (Δ)
- The Greek letter that means 'change in', so ΔC is change in cats.
- rate of change
- How much one quantity changes per unit of another, found by ΔC / ΔT.
Transcript
Jordan is a cat enthusiast. She currently cares for several cats, but she just can't say no to adopting another cute little face. After moving into a bigger house, Jordan started adopting cats at a constant rate. The number of cats in Jordan's house, C, as a function of time since she moved in days, T, is plotted below.
So this Jordan, she just keeps adopting cats. Her house is just getting more and more and more full of cats. I guess that's got to stop at some point. But for this question, they just say she keeps adopting them at a constant rate. So let's look at the choices here and see which of these statements is true.
Jordan had 10 cats when she moved. So let's see this is time from when she moved in. So time equals 0 is right when she moved in her house. And it does look like, yes, she had 10 cats right where she moved in. So that first part of the statement is true. And after moving, she adopted 2 cats each day.
So let's see the rate at which she's adopting cats. And I'm going to find another point on here. So we know that the point 0 comma 10 is on here. So on day 0, when time equals 0, she already had 10 cats, which seems to be more than enough for me. But let's see how many she gets to.
So all of these other ones, it's hard to read. Well, it looks like here, this is definitely on day 15. On day 15, she had 40 cats. So let's see. After 15 days, when her change in time was 15, what was the change in her number of cats? Well, she went from 10 cats to 40 cats.
So she went up to her change in the number of cats-- and we could call that delta C-- is equal to-- she went from 10 to 40. Her change in cats is 30. So her change in cats over change in time is 30 over 15. Or you could say, 2 cats per unit time, per day. So it does look like she got 2 cats per day.
After 15 days at 2 cats a day, she had 30 more cats. She went from 10 to 40. So this statement looks right. And this one is multiple choice. So these other ones are probably wrong. But let's verify that. Jordan had 3 cats when she moved. Well, that's not true.
3 would have been right around here. So that's not right. Jordan had 10 cats when she moved. And after moving, she adopted 1 cat every 2 days. Well, that would be 1/2 a cat a day. And we know that that's not the case. She adopted 2 cats a day. After 15 days, she had 30 cats.
So this isn't right either. Jordan had 3 cats where she moved. Well, we already know that that's not the case. So we know it's the first choice.
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