Question

The equation represents the function f, and the graph represents the function g.

Answer 1

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, $f(x)=3(\frac{5}{2})^x$

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 $y=ab^x$

Put point (1,15)

$15=ab^1=ab$  ......[1]

Put point (0,3)

$3=ab^0=a$ .........[2]

Therefore, a=3 substitute in [1]

$15=(3)b$  

$b=5$

So, The equation of function g is $y=3(5)^x$

The growth rate of function g is 5

The growth rate of function f is $\frac{5}{2}=2.5$

We simply say that the growth factor of g is twice the growth factor of f.

Therefore, Option A is correct.