Question

Which statements are true about exponential decay functions check all that apply

Answer 1

Answer:

The correct statements are:

1) The domain is all real numbers.

4) The base must be less than 1 and greater than 0.

5) The function has a constant multiplicative rate of change.

Step-by-step explanation:

Any function in the form f(x)=ab^x, where a > 0, b > 0 and b not equal to 1 is called an exponential function with base b.

if b>1 then we get a exponential growth function and

We know that a exponential decay function is given as:

f(x)=ab^x with 0<b<1

Hence, the statements that are true about the exponential decay functions are:

1) The domain is all real numbers.

This statement is true since the function is defined for all the real values.

2) As the input increases, the output increases.

This statement is false since from the graph we could check that the exponential decay function decreases with the increasing value of x.

3) The graph is the same as that of an exponential growth function .

The statement is false since the graph of growth function increases with increasing x and is opposite of the decay function.

4) The base must be less than 1 and greater than 0.

This statement is true.

5) The function has a constant multiplicative rate of change.

This option is true.

Since there is a constant multiplicative rate of change (i.e. b)

Answer 2

This is the concept of exponential functions; The statements that are correct about the exponential decay functions are:
1. The domain is all real number
4. The base must be less than 1 and greater than 0
5. The function has a constant multiplicative rate of change