Question

The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5 and x = 7?

A) 5
B) 25
C) 125
D) 625

Answer 1

25 B

Explanation:

What the other person said.

Answer 2

B) 25

Explanation:

Given exponential function:

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

The growth factor between
`x=1` and
`x=3` is 25.

To find the growth factor between
`x=5` and
`x=7`

Solution:

The growth factor of an exponential function in the interval
`x=a` and
`x=b` is given by :

`G=(f(b))/(f(a))`

We can check this by plugging in the given points.

The growth factor between
`x=1` and
`x=3` would be calculated as:

`G=(f(3))/(f(1))`

`f(3)=3(5)^3`

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

Plugging in values.

`G=(3(5)^3)/(3(5)^1)`

`G=((5)^3)/((5)^1)` (On canceling the common terms)

`G=(5)^((3-1))` (Using quotient property of exponents
`(a^b)/(a^c)=a^((b-c))` )

`G=(5)^(2)`

∴
`G=25`

Similarly the growth factor between
`x=5` and
`x=7` would be:

`G=(f(7))/(f(5))`

`f(7)=3(5)^7`

`f(5)=3(5)^5`

Plugging in values.

`G=(3(5)^7)/(3(5)^5)`

`G=((5)^7)/((5)^5)` (On canceling the common terms)

`G=(5)^((7-5))` (Using quotient property of exponents
`(a^b)/(a^c)=a^((b-c))` )

`G=(5)^(2)`

∴
`G=25`

Thus, the growth factor remains the same which is =25.