[Video] Q24: In the xy-plane, the graph of a linear equation of the form y = mx + b and the graph of an exponential equation of the form y = ab^x both contain points (1, 3) and (2, 4). if the point (r, s) is on the graph of the linear equation and the point (r, t) is on the graph of the exponential equation, where 0 < r < 4 and s > t, which of the following must be true?

Explanation for Question 24 From the Math (Calc) Section on the 2019 April Sat

And number 24, we were told that the graph of the linear equation, 2 Y equals MX plus B and the graph of the exponential equation, 3 Y equals AB to the X, both have points one, 4 three, and two, four. Then we want to know if the point RS is 5 on the graph of the linear equation. And the point RT is on the 6 graph of the exponential equation, where zero is less than ours, 7 less than four, and S is greater than T which of the following must 8 be true. So the best way to start this one would be to draw 9 a picture. So I will quickly sketch out a coordinate plane. 10 It doesn't have to be perfect, especially if you don't have that much time. 11 So let me at least try to make that look a little better. 12 All right. So now we can get the points of one, 13 three and two, four on our graph there. 14 Now I'm going to use blue for the linear equation. 15 So let me draw a line through those points and I'll use red 16 for exponential. So an exponential through those points would look 17 something like this. 18 Again, it doesn't have to be perfect as long as you understand what is 19 going on. And the key thing to understand here is that right 20 in between these two points is where the linear is greater than the exponential. 21 At every other point, the exponential is greater than linear, 22 but we can see it switches here as the exponential kind of dips below 23 the linear in order to connect the two points. 24 So now the point R S is on the graph of the linear and 25 RT is on the graph of the exponential where zero is less than R 26 is less than four. So R has to be between 27 zero and four. And the important one is 28 that as has to be greater than T. So the Y value of the 29 linear has to be greater than the Y value of the 30 exponential. And we said before that that happens right here in between the two 31 points as the exponential dips below. 32 So that means our has to be in between the 33 X coordinates of one and two. 34 So the correct answer will be B.