Question

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

f(x)=3(5/2)^x

Determine the relationship between the growth factors of f and g.

A. The growth factor of g is twice the growth factor of f.
B. The growth factor of f is twice the growth factor of g.
C. The growth factor of f is 2.5 times the growth factor of g.
D. The growth factor of f is the same as the growth factor of g.

Answer 1

Option A- The growth factor of g is twice the growth factor of f.

Explanation:

Given : The equation represents the function f,
`f(x)=3((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
`(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.