Answer:
Option A- The growth factor of g is twice the growth factor of f.
Step-by-step explanation:
Given : The equation represents the function f, [tex]f(x)=3(\frac{5}{2})^x[/tex]
and the graph represents the function g.
To determine : The relationship between the growth factors of f and g.
Solution : First we see that the function g represent in the graph is the exponential growth rate.
So, we can find out the equation of g by looking the points in the graph
The line passing through the points (1,15) and (0,3)
Forming exponential equation from the points.
General form of exponential equation is [tex]y=ab^x[/tex]
Put point (1,15)
[tex]15=ab^1=ab[/tex] ......[1]
Put point (0,3)
[tex]3=ab^0=a[/tex] .........[2]
Therefore, a=3 substitute in [1]
[tex]15=(3)b[/tex]
[tex]b=5[/tex]
So, The equation of function g is [tex]y=3(5)^x[/tex]
The growth rate of function g is 5
The growth rate of function f is [tex]\frac{5}{2}=2.5[/tex]
We simply say that the growth factor of g is twice the growth factor of f.
Therefore, Option A is correct.
