Question

128. Identify which functions are exponential. For the functions that are exponential, use the properties of exponents to identify the percent rate of change, and classify the functions as indicating exponential growth or decay.

b.g(x) = 3/4x

Answer 1

g(x) is an exponential decay function.

Explanation:

Given : Function
`g(x)=((3)/(4))^x`

To find : Identify the exponential function and classify the functions as indicating exponential growth or decay ?

Solution :

An exponential function is a nonlinear function of the form
`y = ab^x`, where a ≠ 0, b ≠ 1, and b > 0.

1) When a > 0 and b > 1, the function is an exponential growth function.

2) When a > 0 and 0 < b < 1, the function is an exponential decay function.

On comparing with general function,

The given function
`g(x)=((3)/(4))^x` is an exponential function.

Where, a=1 and
`b=(3)/(4)`

Here,
`b=(3)/(4)=0.75`

i.e. 0<0.75<1 means function is a decay function.