Comparing exponential functions with the same growth factor
About this video
Three functions J, K and L all have the growth factor 1.8 but different starting values: 3, 9 and 6. The video matches each to its graph by evaluating at x = 0, using the fact that 1.8^0 = 1. With the same growth factor, the highest starting value gives the highest curve.
You'll be able to
- find the starting value of an exponential function by evaluating at x = 0.
- match exponential equations to graphs using their starting values.
- explain why functions with the same growth factor keep their order.
Key words
- growth factor
- The number you multiply by each time x goes up by 1; here, 1.8.
- starting value (initial value)
- The output when x = 0; the number in front of the growth factor.
Transcript
- [Instructor] So right over here we've defined three functions. We have the equations for three different functions, J, K, and L. And over here, we have the graphs of those three functions, but what we wanna figure out is which function corresponds to which graph.
So pause this video, have a go at this before we do it together. Okay, so when we look at this, when we look at the equations, they all have the same growth factor. We have something times 1.8 to the X for every one of them. And so what's different is this something.
And so one way to think about it is where are they starting? And one way to think about where are they starting is what happens when X equals zero? Well, when X equals zero, let's just do it this way. J of zero is gonna be three times 1.8 to the zero, three times 1.8 to the zero.
1.8 to zero is just one, so it's equal to three. By the same logic, K of zero is just gonna be nine times 1.8 to the zero, which is equal to nine. And L of zero is equal to six times 1.8 to the zero, which is just six. And so when X equals zero, which one is equal to three?
Well, that's this red one, that's C. So this one is going to be J. And then which one is equal to six? At X equals zero, as we see right over here, that one is L. And then last but not least, A, which is equal to nine at x equals zero, that is K. Another way you could have thought about it is they all have the same growth factor.
Every time X increases by one, our function is going to be increasing by a factor of 1.8 and so what really is just the difference of the starting point and the one that has the highest starting point, which is K, is gonna be the highest function, which you can see is function A.
And then the one with the lowest starting point is gonna be the lowest function. And the one in between is going to be the one in the middle L right over there.
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