Question

When x increases from a to a + 2, y increases by a factor of 16.

For which functions is this statement true?
A) y = 2(4)x
B) y = 4x + 2
C) y = 2(16)x
D) y = 16x + 2

Answer 1

The answer is A) y=2(4)x

Answer 2

Correct option is A.

Explanation:

Given x increases from a to a + 2, y increases by a factor of 16.

we have to find the function for which the above statement is true.

Option A:
`y = 2(4)^x`

`f(x)=2(4)^x`

⇒
`f(a)=2(4)^a`

⇒
`f(a+2)=2(4)^(a+2)`

⇒
`f(a+2)=2(4^2)4^a`

⇒
`f(a+2)=16f(a)`

⇒ When x increases from a to a + 2, y increases by a factor of 16.

Hence, option A is correct.