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Exponential Regression

Master exponential regression with interactive lessons, including scatterplots and best-fit curves to model data of the form y = a b^x. Designed for students like you!

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Exponential Regression

Study Guide

Key Definition

Exponential regression determines the best-fit exponential curve of the form $y = a b^x$ for a given data set, typically by minimizing the sum of squared residuals.

Important Notes

Initial value $a$ can be any nonzero real number, often taken positive when modeling growth scenarios
Growth scenarios use base $b > 1$
Decay scenarios use base $0 < b < 1$
When $a$ > 0, outputs remain positive and never reach zero
Exponential regression can model finance, population growth, radioactive decay, and more

Mathematical Notation

$y = a b^x$ defines how output depends on exponentiating $b$ and scaling by $a$

$a$ represents the initial value (scale factor)

$b$ represents the growth or decay factor

$x$ is the exponent (independent variable)

Remember to use proper notation when solving problems

Why It Works

Exponential regression captures real-world phenomena where the rate of change is proportional to the current amount, fitting a curve to data with constant percentage growth or decay.

Remember

Exponential models are key tools for analyzing processes with proportional change over time, from finance to biology.

Quick Reference

Exponential Growth:$b > 1$

Exponential Decay:$0 < b < 1$

Understanding Exponential Regression

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Exponential regression finds an exponential function of the form $y = a b^x$ that best fits a given data set, giving insight into constant-percentage growth or decay.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the initial value in the function $y = 2 \times 3^x$?

Real-World Problem

Question Exercise

Intermediate

Bacteria Growth Scenario

A population of bacteria triples every hour. If you start with 100 bacteria, express this growth using exponential regression.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Explore how the function $y = a \times b^x$ changes if $b$ is between 0 and 1.

Challenge Quiz

Single Choice Quiz

Advanced

In the function $y = 5 \times (0.5)^x$, what does $0.5$ represent?

Recap

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Review key concepts and takeaways