00:01
So in this question, we said the table below shows some values of a linear function f and an exponential function g.
00:07
We want to fill in exact values for each of the missing entries.
00:13
And so i believe that you have exactly the right idea for f of x, okay? so in f of x, since the function is linear, you're going up by the same amount each time.
00:26
And so you go up a total of 100 over the course of the 4x value.
00:33
So you find your slope, which is 125 minus 25 over 4 minus 0.
00:46
100 over 4 gives you 25.
00:50
That means every time your x goes up by 1, your y goes up by 25.
00:56
And so you are correct with these values of 50, 75, and 100.
01:05
Now for gx, you have an exponential function, and these were the values that were a little bit off, even though you were on the right track.
01:16
So what do we do in an exponential function? to move to the right by one unit always multiplies by the same number.
01:28
So with a linear function, notice you were adding 25, adding 25, adding 25, adding 25, adding 25, with an exponential function, we're always multiplying by the same number, which we'll often call r.
01:49
Okay? and so, we're multiplying by r to move from one term to the next...