# Derivatives of Exponential Function Teacher Resources

Find Derivatives of Exponential Function educational ideas and activities

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#### An Introduction to Exponential Functions

Construct tables of values to understand constant percent growth rate in an exponential function. This lesson contains a handout to different problems that help provide insight into exponential functions.

#### Explore Learning Exponential Functions

High schoolers graph exponential equations and solve application problems using exponential functions. They re-enact a story about a peasant worker whose payment for services is rice grains doubled on a checker board. They place M & Ms on a checkerboard and mark the number on a graph. They double the number for each space on the board and create a graph of the data.

#### An Introduction to Exponential Functions

Students identify exponential functions. For this algebra lesson, students rewrite word problems and solve using the properties of Exponential Functions. They graph and solve exponential equations.

#### Exponential Functions

Students graph exponential equations of the form y=Ma. They understand the effects of M, a, and k on the graph. They solve application problems using exponential functions.

#### Comparing Investments

Money, money, money. A complete instructional activity that makes use of different representations of simple and compound interest, including written scenarios, tables, graphs, and equations to highlight similarities and differences between linear and exponential functions.

#### Extending the Definitions of Exponents, Variation 2

Introduce the concept of exponential functions with an activity that extends the definition of exponents to include rational values. Start with a doubling function at integer values of time, then expand table to include frational time units. Lesson includes a detailed commentary on how to work each problem.

#### Modeling Natural Disaster with Mathematical Functions

Ninth graders investigate the functional relationship of different environmental phenomena. In this math lesson, 9th graders create models of various natural disasters. They use logarithmic and exponential functions to interpret population growth.

#### An Introduction to the TI-Nspire Calculator Function

Students explore the calculator function of the TI-Nspire.  In this secondary mathematics lesson, students investigate many of the features of the calculator function of the TI-Nspire.  Students review basic computation, square roots, absolute values, exponential functions, logarithmic functions, trigonometric functions, summations and matrices as they explore the TI-Npsire.

#### Derivatives of Exponential Functions

Students take derivatives of exponential functions.  In this taking derivatives of exponential functions instructional activity, students prove the derivative of an exponential function is the exponential function.  Students find derivatives where the base is a constant and the exponent is a variable.

#### Product Rule

Sal defines the product rule and then shows two examples of how it is used. He then shows an example of finding the derivative by using both the chain rule and product rule together.

#### Investigation the Derivatives of Some Common Functions

Students investigate the derivative of a function.  In this calculus lesson, students explore the derivatives of sine, cosine, natural log, and natural exponential functions.  The lesson promotes the idea of the derivative as a function and uses numerical and graphical investigations to form conjectures about common derivative formulas.

#### Exponential Decay

Students study exponential decay and its application to radiocarbon dating. In this exponential decay lesson, students use candy to model the time it takes for something to decay. Students also graph the data they collect and describe using an algebraic formula that gives the age of an object as a function.

#### How High Does a Ball Bounce?

Ninth graders investigate exponential regression.  In this Algebra I lesson plan, 9th graders explore the rebound heights of a racquetball bouncing and develop an exponential data model.  The lesson plan is intended to be an introduction to exponential regression.

#### Computing Derivatives

Twelfth graders investigate derivatives.  In this calculus lesson plan, 12th graders use technology to explore the basic derivatives and how to choose the proper formula to use them.  The lesson plan requires the use of the TI-89 or Voyage and the appropriate application.

#### Making Piecewise Functions Continuous and Differentiable

Students explore the concept of piecewise functions.  In this piecewise functions lesson, students discuss how to make a piecewise function continuous and differentiable.  Students use their Ti-89 to find the limit of the function as it approaches a given x value.  Students find the derivative of piecewise functions.

#### Lesson #55 Test on Logarithms and Exponentials

Twelfth graders assess their knowledge of logarithmic and exponential functions.  In this calculus lesson, 12th graders demonstrate their knowledge of all concepts of logarithmic and exponential functions.  Students apply the derivatives of the logs and exponential functions.

#### Complex Analysis: Complex Exponential

In this complex exponential worksheet, students identify an entire function and explore how to show a function is analytic. This two-page worksheet contains four problems, as well as explanations and examples.

#### New Functions From Old, Part 1

In this function worksheet, students use various methods to solve functions. They explore the logarithm function, the derivative of an exponential function, and compose a function with a linear equation. This four-page worksheet contains explanations, examples, and four problems.

#### Shedding Light on the Subject: Function Models of Light Decay

Young scholars develop and analyze exponential models for the behavior of light passing through water.

#### Exponential Decay Formula (can skip, involves Calculus)

Sal continues his discussion of decay by showing students the math involved in determining how much a substance is left after one half-life, two half-lives, and even three half-lives have gone by. He sets up a general function of time that can be used to determine the remaining amount of a substance after 10 minutes, or three billion years have elapsed!