Question

question: concerning an exponential decay function: check all that apply:
the domain is all real numbers.
as the x - value increases, the y - value decreases.
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 multiplication rate of change.

Explanation:

1. Domain is all real numbers: Exponential functions (including decay) have a domain of all real numbers, as you can raise a positive base to any real exponent.
2. As input increases, output decreases: For exponential decay functions of the form $f(x)=ab^x$ where $0
3. The base must be less than 1 (and greater than 0): By definition, exponential decay functions have a base $b$ such that $0
4. Constant multiplicative rate of change: Exponential functions (decay included) change by a constant multiplicative factor for each unit increase in input, which is the base $b$.
5. Graph is NOT the same as exponential growth: Exponential growth graphs increase as input rises, while decay graphs decrease, so their graphs are different.

Answer:

Check all of the following:

• The domain is all real numbers
• As the input increases, the output decreases
• The base must be less than 1 (and greater than 0)
• The function has a constant multiplicative rate of change