Exponential Functions
Graph and solve exponential growth and decay problems
lessons (2)
Introduction to Exponential Functions
Learn what exponential functions are, how they differ from linear and polynomial functions, and why they model explosive growth and decay.
Exponential Growth
Learn how quantities grow exponentially and apply growth formulas to real-world scenarios.
Exponential functions model rapid growth or decay where the rate of change is proportional to the current amount. From compound interest to population growth to radioactive decay, these functions describe many natural phenomena.
What Students Will Learn
- Graph exponential growth and decay functions
- Identify key features of exponential graphs
- Write exponential equations from context
- Solve exponential equations
- Apply to real-world growth and decay problems
Frequently Asked Questions
What makes a function exponential?
In exponential functions, the variable is in the exponent: $f(x) = a \cdot b^x$. The base b determines growth (b>1) or decay (0<b<1).
What is the difference between linear and exponential growth?
Linear growth adds a constant amount each period. Exponential growth multiplies by a constant factor, causing much faster increases.
What is the natural exponential function?
$f(x) = e^x$ where e ≈ 2.718. It appears naturally in continuous growth and calculus.