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

Answer:

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

Step-by-step 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).

$3=ab^0$

$a=3$

$12=3(b)^1$

$b=\frac{12}{3}=4$

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

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).

Answer 2

Hello there! I had the same question and my answer was less than. I am not positive that it is correct but that's my answer so please tell me if I am wrong.

Thank you and have a great day!