Question

10. Select all that are true for the graph that represents

the function f(x) = 5(3)^x
A. The graph is increasing by a common ratio of 3.
B. The graph is decreasing by a common ratio of 3.
C. As x increases, y increases.
D. As x increases, y decreases.
E. As x decreases, y approaches 1.
F. As x decreases, y approaches 0

Answer 1

A, C and F

Explanation:

The given function is

`f(x)=5(3)^x`

It is an exponential function of the form

`f(x)=a(b)^x`

On comparing both the functions, we get

`a=5,b=3`

It means the initial value is 5 and growth factor is 3.

Since both values are positive it means the given functions is an exponential growth function, therefore,

1. The graph is increasing by a common ratio of 3.

2. As x increases, y increases.

3. As x decreases, y approaches 0.

Hence, the correct options are A, C and F.