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Derivatives of Exponential Function Teacher Resources
Find Derivatives of Exponential Function educational ideas and activities
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.
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.
Twelfth graders investigate the derivative of a function. In this calculus lesson, 12th graders 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.
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.
High schoolers 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. High schoolers review basic computation, square roots, absolute values, exponential functions, logarithmic functions, trigonometric functions, summations and matrices as they explore the TI-Npsire.
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.
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!
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.
In this radiation and temperature worksheet, students use 2 methods to derive the Wein Displacement law that shows the relationship between the temperature of a body to the frequency where the Planck curve's value is at its maximum. Students are given data of the temperatures and wavelengths for 12 different bodies and they find a formula that fits the data.