Question

Given the function f(x)=abx

Identify the base b, if the graph passes through the point (1,6)
and (2,18)
(1 point)
Responses

5
5

2
2

4
4

3

Answer 1

The base, b, can be found by plugging in the x and y values from one of the given points into the equation and solving for b.

Using the point (1,6):

f(1) = ab(1) = 6
ab = 6

Using the point (2,18):

f(2) = ab(2) = 18
2ab = 18

To solve these two equations, we can divide the second equation by 2:

ab = 6
ab = 9

Since both equations are equal to ab, we can set them equal to each other:

6 = 9

This equation has no solution, which means that there is no base that satisfies both of the given points. Therefore, there is no valid base for the function f(x) = abx.