Question

What is the rate of increase for the function f(x)=1/3(3sqr24)^2x

A.1/3

B.2 3sqr3

C.4

D. 4 3sqr9

Answer 1

D

Explanation:

Took the test

Answer 2

The correct option is D.

Explanation:

The general form of exponential function is

`f(x)=ab^x` ... (1)

Where a is initial value and b is rate of increase.

The given function is

`f(x)=(1)/(3)(\sqrt[3]{24})^(2x)`

`f(x)=(1)/(3)(\sqrt[3]{2^3\cdot 3})^(2x)`

`f(x)=(1)/(3)(2\sqrt[3]{3})^(2x)`

`f(x)=(1)/(3)((2\sqrt[3]{3})^2)^(x)`

`f(x)=(1)/(3)(4\sqrt[3]{3^2})^(x)`

`f(x)=(1)/(3)(4\sqrt[3]{9})^(x)` .... (2)

From (1) and (2), we get

`b=4\sqrt[3]{9}`

Therefore the correct option is D.