Question

An image with a graph, the curved line starts at (-40, 0) and remains constant along the x-axis, then makes a sharp curve at (-1, 0) and continues to rise steeply until (2, 40)

What would an equation for this graph be?

y = 10(4)^x
y = 3.5(4)^x
y = -3.5(4)^x
y = 50(4)^x

Answer 1

Check which fits the point (2,40). For y = a·4^x we have a·4^2 = 16a ≈ 40 ⇒ a ≈ 40/16 = 2.5, which is not an option. Now evaluate the choices at x=2:

- 10·4^2 = 160
- 3.5·4^2 = 56
- −3.5·4^2 = −56 (wrong sign)
- 50·4^2 = 800

The only positive, small-coefficient exponential that stays near 0 for large negative x and then rises steeply is y = 3.5(4)^x. (Strictly speaking none of the given options passes exactly through (2,40); the exact fit would be y = 2.5·4^x.)