Question

Which function represents exponential decay?

Answer 1

Answer:

Option: D is the correct answer.

         D)  $f(x)=4\cdot (\dfrac{2}{3})^x$

Step-by-step explanation:

We know that a exponential function is in general represented by:

       $f(x)=ab^x$

where a>0 and b is called the base of the function and x is the exponent.

and if b>1 then the function is a exponential growth function

and 0<b<1 then the function is a exponential decay function.

A)

$f(x)=\dfrac{1}{2}\cdot (\dfrac{3}{2})^x$

This is a exponential growth function.

Since,

$b=\dfrac{3}{2}>1$

B)

$f(x)=\dfrac{1}{2}\cdot (\dfrac{-3}{2})^x$

This is not a exponential function because b is not strictly greater than zero.

C)

$f(x)=4\cdot (\dfrac{-2}{3})^x$

This is also not a exponential function because b is not strictly greater than zero.

D)

$f(x)=4\cdot (\dfrac{2}{3})^x$

This is a exponential decay function.

Because it fulfills the condition of the exponential decay function.

Since,

$b=\dfrac{2}{3}$

Answer 2

Answer:

D

Step-by-step explanation:

Exponential decay occurs when the base is less than 1 but greater than 0.

3/2 = 1.5 and is greater than 1.

-3/2 is not greater than 0 and is not exponential

-2/3 is not greater than 0 and is not exponential

2/3 is less than 1 and greater than 0. This is decay.