Question

The graph of an exponential model in the form y = a ⋅ bx passes through the points (3, 5) and (4, 10). Which point is also on the graph?

Answer 1

The point (1, 1.5625) is also on the graph.

Step-by-step explanation:

The given exponential model is y = a ⋅ bx. We are given two points on the graph, (3, 5) and (4, 10). Using these points, we can form a system of equations to solve for the values of a and b.

By substituting the coordinates of the points into the equation, we get:
5 = a ⋅ b^3 and 10 = a ⋅ b^4.

Solving these equations simultaneously, we find that a = 0.78125 and b = 2. This means that the equation for the graph is y = 0.78125 ⋅ 2^x. Substituting x = 1 into this equation, we find that y = 1.5625, so the point (1, 1.5625) is also on the graph.

Answer 2

The answer is D

Step-by-step explanation:

First, find a and b from the given points.

y = abx

5 = ab3

10 = ab4

b = 10/5 = 2

5 = a(23)

a = 5/8

y = (5/8) 2x

Test the choices:

x = 2 ⇒ y = 5/2

This rules out (a) and (b).

x = 5 ⇒ y = 20