y = ax, where a is greater than zero but not equal to 1 and x is an exponent
1. exponential decay
2. exponential function
3. exponential growth
I disagree. I prefer 2: exponential function.
If 0 < a < 1 then a^x is exponential decay
You are correct. If 0 < a < 1, then y = ax^k is an exponential decay function. Thank you for catching my mistake!
The equation y = ax, where a is greater than zero but not equal to 1 and x is an exponent, represents an exponential function.
To understand why, let's break down the terms:
- "y" represents the dependent variable or the output of the function.
- "a" is the base of the exponent and determines the rate of growth or decay.
- "x" is the exponent, which can be positive or negative and determines the amount of growth or decay.
An exponential function is a mathematical function in which the independent variable (x) appears in the exponent. It is commonly written in the form y = ab^x, where a and b are constants. However, in this case, since a is the base itself, the equation y = ax represents an exponential function with a constant base.
Now, as for the nature of the function, whether it represents exponential decay, exponential growth, or something else, it depends on the value of a.
- If a is between 0 and 1 (exclusive), the function represents exponential decay. The values of y will decrease as x increases.
- If a is greater than 1, the function represents exponential growth. The values of y will increase as x increases.
In this case, since a is greater than zero but not equal to 1, the equation y = ax represents an exponential growth function.