Question

Which statements are true about exponential decay functions? Check all that apply. The domain is all real numbers. As the input increases, the output increases. The graph is the same as that of an exponential growth function. The base must be less than 1 and greater than 0. The function has a constant multiplicative rate of change.

Answer 1

A D E

Explanation:

Edge2020

Answer 2

The correct options are:

• The domain is all real numbers.

• The base must be less than 1 and greater than 0.

• The function has a constant multiplicative rate of change.

Explanation:

We know that the exponential function is given by:

`f(x)=ab^x`

where a>0 and b are constants.

Also, it represents a growth function if b>1

and a decay function if 0<b<1

where b is the base.

• x belongs to whole of the real numbers( since the exponential function is well defined for all the real values of x.

Hence, the domain of the function is all the real numbers )

• Also, the graph of a decay function decreases continuously i.e. with the increasing input value the output value decreases.

• The exponential decay function always have a constant multiplicative rate of change i.e. b.