What are Exponential Functions?
- Exponential functions are any function where a constant is brought to the power of x.
- As x is the variable that changes in a graph, the power to which the constant is bought to changes with x, resulting in an upwards or downwards slope depending on the constant.
Exponential Growth Functions
- Exponential growth functions are functions where a constant greater than one is bought to the power of x.
- As x increases, in value, the power also increases, leading to exponential growth.
- Their graphs resemble an upwards slope that never goes below the x-axis.
- Adding a negative in front of the constant causes the function to flip relative to the x-axis.
Exponential Decay Functions
- Exponential decay functions are like exponential growth functions, except the constant is greater than zero but less than one.
- This means the number gets smaller the greater the power it is bought to is.
- Their graphs look like a downward slope that never goes below the x-axis.
- They look like an exponential growth function flipped relative to the y-axis.
- The value "decays" as it gets smaller and smaller.
- Adding a negative in front of the constant causes the function to flip relative to the x-axis.
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