Question

Here are graphs of three exponential equations.

Match each equation with its graph.
6,000
4,000
2,000
Column A
1.
2
3
-
f(x) = 100 (3)^x
g(x) = 100 (35)^x
h(x) = 100 (4)^x
B
U
3
Column B
a. C
b. A
C. B

Answer 1

f(x) = 100 (3)^x <===> C

f(x) = 100 (3.5)^x <===> B

f(x) = 100 (4)^x <===> A

Explanation:

Since the base of each of the exponential functions is the same, the higher the base, the higher up the graph will be with respect to another base with a lower value

This can be easily determined by choosing a specific value for x for each equation and seeing what the f(x) value is

Let's choose x = 2

For f(x) = 100 (3)^x, at x = 2 we get f(2) = 100(3)^2 = 100 x 9 = 900

For f(x) = 100 (3.5)^x, at x = 2 we get f(2) = 100(3.5)^2 = 100 x 12.25 = 12.25

For f(x) = 100 (4)^x, at x = 2 we get f(2) = 100(4)^2 = 100 x 16 = 1600

So for a specific value of x, the higher the base, the higher the graph is relative to the x-axis

So the matches are:

f(x) = 100 (3)^x <===> C

f(x) = 100 (3.5)^x <===> B

f(x) = 100 (4)^x <===> A