Exponential Functions
An exponential function has the form y = a^x where a > 0. These functions model growth (a > 1) and decay (0 < a < 1) and appear in finance, science, and medicine.
What You Need to Know
An exponential function has the form y = a^x where a > 0. These functions model growth (a > 1) and decay (0 < a < 1) and appear in finance, science, and medicine.
Key Concept Diagram
y = a^x with a > 1 models exponential growth (curve rises steeply)
y = a^x with 0 < a < 1 models exponential decay (curve falls toward zero)
The y-intercept is always 1 since a^0 = 1
The x-axis is a horizontal asymptote; the function never reaches zero
Key Vocabulary
Exponential function
A function of the form y = a^x where the variable is the exponent
Growth
An exponential function where values increase rapidly over time
Decay
An exponential function where values decrease toward zero
Asymptote
A line that the graph approaches but never reaches
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the y-intercept of y = 3^x?
Question 2
Which function represents exponential decay?
Question 3
As x increases, the graph of y = 4^x:
Key Concepts Summary
- ●y = a^x with a > 1 models exponential growth (curve rises steeply)
- ●y = a^x with 0 < a < 1 models exponential decay (curve falls toward zero)
- ●The y-intercept is always 1 since a^0 = 1
- ●The x-axis is a horizontal asymptote; the function never reaches zero