Question

y = 2x shows
✔ exponential growth.
Look at the black points on the graph. Fill in the missing coordinates for y = 2x.
(0,
1
) and (
5
, 32)
Look at the orange points on the graph. If the x-values a and c are 1 unit apart, how are the y-values b and d related?

Answer 1

I think you mean y = 2^x (exponential). The missing black-point coordinates are correct:
- (0, 1) because 2^0 = 1
- (5, 32) because 2^5 = 32

For the orange points: if the x-values a and c differ by 1 (say c = a + 1), then the y-values satisfy
d = 2^c = 2^(a+1) = 2·2^a = 2·b.
So the y-value at the x one unit to the right is twice the other. (If the one-unit step is the other direction, the relation is reversed.)