MathIsimple

Exponential Functions & Models

Master exponential functions, understand growth and decay, learn transformations, and apply exponential models to real-world problems.

11th Grade
Functions
~60 min
🎮 Interactive Activity: Exponential Value Calculator

Calculate the value of the exponential expression!

Expression:

2^3 = ?
🎮 Interactive Activity: Growth/Decay Identifier

Identify if the function represents growth or decay!

Function:

f(x) = 2ˣ

Type:

?
1. Exponential Function Definition

What is an Exponential Function?

An exponential function has the form f(x) = a · bˣ, where a is a constant, b > 0 and b ≠ 1 is the base, and x is the exponent.

Example 1: Basic Exponential Function

f(x) = 2ˣ

• Base: 2 (greater than 1, so it's growth)

• f(0) = 2⁰ = 1 (y-intercept)

• f(1) = 2¹ = 2

• f(2) = 2² = 4

• As x increases, f(x) grows rapidly

Example 2: Exponential with Coefficient

f(x) = 3 · 2ˣ

• Coefficient: 3

• Base: 2

• f(0) = 3 · 2⁰ = 3 · 1 = 3

• The coefficient affects the y-intercept but not the growth rate

2. Properties of Exponential Functions
3. Transformations of Exponential Functions
4. Exponential Growth and Decay
5. Real-World Applications
Frequently Asked Questions

Practice Time!

Practice Quiz
10
Questions
0
Correct
0%
Score
1
What is the value of 2³ × 2⁴?
2
Simplify: (3²)⁴
3
What is f(2) if f(x) = 3ˣ?
4
Which function represents exponential growth?
5
What is the y-intercept of f(x) = 4ˣ?
6
If a population doubles every 5 years, what is the growth factor?
7
What is the horizontal asymptote of f(x) = 2ˣ + 3?
8
Simplify: 5ˣ / 5²
9
What is the domain of f(x) = 3ˣ?
10
If f(x) = 2ˣ, what is f(-1)?