Question

The table shows the function ​ g(x) ​ . Select from the drop-down menu to correctly compare the growth factors for the exponential functions g(x) and f(x)=4(3)x .

x: 0, 1, 2
g(x): 3, 12, 48

Is the growth factor greater than, lesser than, or equal to the growth factor of g(x)?

Answer 1

f(x) is less than the growth factor of g(x).

Explanation:

Answer 2

The growth factor of f(x) is less than the growth factor of g(x).

Explanation:

The general form of exponential function is

`h(x)=ab^x`

Where, a is the initial value and b is the growth factor.

The given function is

`f(x)=4(3)^x`

The initial value of f(x) is 4 and the growth factor is 3.

From the given table it is noticed that the function g(x) is passing through the points (0,3), (1,12), (2,48).

`3=ab^0`

`a=3`

`12=3(b)^1`

`b=(12)/(3)=4`

`g(x)=3(4)^x`

The initial value of g(x) is 3 and the growth factor is 4.

Therefore the growth factor of f(x) is less than the growth factor of g(x).