Exponential Functions What is an exponential function Exponential

Exponential Functions

What is an exponential function? Exponential functions represent situations that are growing exponentially Where do we see exponential functions in everyday life?

Examples of Exponential Functions Population Growth Money (Compound Interest) Depreciation (Cars) Half-Life (Radioactive Material) Bacteria Growth

Definition of Exponential Function y = bˣ Question: How is this function different than functions we have previously worked with?

Answer: The exponent is the variable! y = bˣ b is the Base and is a positive number x is the exponent and is a variable. It can be any number Question…. Is y = x³ an exponential function? NO!!

The graph of an exponential function One of the most common exponential functions is: y = 2ˣ The graph looks like this:

Properties of Graphs Y-Intercept Asymptote Increasing/Decreasing

Properties of Graphs Y-Intercept – where does the function cross the y-axis? Set x = 0 Asymptote – a line that continually approaches a curve but doesn’t meet it Increasing/Decreasing – is the function increasing or decreasing?

y = 2ˣ Y-intercept – This function crosses the y-axis at (0, 1) The asymptote of this function is the x-axis, or the line y = 0 This graph is increasing

y = 3ˣ Y-intercept – the function crosses the y-axis at (0, 1) The asymptote of this function is the x-axis, or the line y = 0 The graph is increasing

Other Exponential Graphs How would we show a decreasing exponential function? How would we represent depreciation using an exponential graph? What would be different about the equation y = bˣ compared to the ones we have seen already?

How would the equation of this decreasing exponential function be different than y = 2ˣ, y = 3ˣ, y = 5ˣ ? What is the y-intercept and asymptote?

Y-Intercept – the function crosses the y-axis at (0, 1) The asymptote is the x-axis, or the line y = 0 This graph is decreasing We call a graph like this exponential decay