Exploring exponential situations as functions
About this video
A table shows the number of duckweed plants P after D days. The video explains that a relationship is a function if each input has exactly one output, and since every day value has exactly one plant count, P is a function of D. It also shows that 'always increasing' is not the reason something is a function.
You'll be able to
- decide whether a table represents a function.
- explain that a function gives exactly one output for each input.
- spot a wrong reason for calling something a function.
Key words
- function
- A relationship where each input has exactly one output.
- input
- The value you start with; here, the number of days D.
- output
- The value you get; here, the number of plants P.
Transcript
- [Instructor] We're told the table shows the number of duckweed plants, P, after D days of growth in a marsh under ideal conditions. For each day, number of days, it tells us how many plants have grown. Is the number of plants P, a function of the days, D? Why or why not?
So why don't you pause this video, have a go at this before we do this together. All right, now let's do this together. So when we think about a function, it sounds like a very fancy thing, and it is very useful, but it really is just the notion that, for any input, are we going to have a unique output?
And so we can see here that, for each input, I only have one output right over here. Zero goes to two, two goes to four, four goes to eight, six goes to 16, eight goes to 32, 10 goes to 64, so this is a function! So you might be saying, wait, well, how could it not be a function?
Well, if I said that four could go to eight, and then if I had another entry here that four could also go to 16, then we would have a problem, because then I would have two, I would have the same input leading to two different outputs, which would say that you can't be a function, but this one definitely is a function, so let's see which of these choices.
It's gonna be one of these two that say yes. "Yes, because the number of plants always increases, it must be a function." No, that's not. Just because something increases doesn't mean it has to be A. It doesn't mean that it has to be a function. Let's see. "Yes, each day value, D, has exactly one plant total, so each input has only one output."
Yes. I like that one right over there.
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