Question

The graph 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)=5(3)^x .

The growth factor of​ f(x) is ___ the growth factor of ​ g(x) ​.


A: Greater Than

B: Less Than

C: Equal To

Answer 1

The answer is less than.

Answer 2

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

Explanation:

The growth factor of a function h(x)=a(b)^x is b.

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

The growth factor of f(x) is 3.

2) g(x)=a(b)^x

when x=0, g(0)=1→a(b)^0=1→a(1)=1→a=1

g(x)=1(b)^x→g(x)=(b)^x

when x=1, g(1)=5→(b)^1=5→b=5

g(x)=(5)^x

The growth factor of g(x) is 5.

The growth factor of f(x)=3 is less than the growth factor of g(x)=5