Question

Which equation represents exponential growth f(x)=4(0.07)^x , f(x)=2(0.44), f(x)=1/2(6)^x, f(x)=7(1/2)^x

Answer 1

`f(x)=(1)/(2)(6)^x`

Explanation:

An exponential function is of the form
`y=ab^(x)`, where,
`a\\e 0`.

Now, if a > 0 and b > 1, then the exponential function represent exponential growth.

If a > 0 and 0 < b < 1, then the exponential function represent exponential decay.

Let us check each function now.

Option 1:
`f(x)=4(0.07)^x`

Here,
`a=4,b=0.07`

As 0.07 < 1, the function is exponential decay.

Option 2:
`f(x)=2(0.44)^x`

Here,
`a=2,b=0.44`

As 0.44 < 1, the function is exponential decay.

Option 3:
`f(x)=(1)/(2)(6)^x`

Here,
`a=(1)/(2),b=6`

As 6 > 1, the function is exponential growth.

Option 4:
`f(x)=7((1)/(2))^x`

Here,
`a=7,b=(1)/(2)`

As
`(1)/(2)< 1`, the function is exponential decay.

Therefore, the equation that represent exponential growth is
`f(x)=(1)/(2)(6)^x`