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Derivatives of Exponential Function Teacher Resources
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In this differentiating special functions worksheet, students solve and complete 5 various types of problems. First, they differentiate each of the given functions. Then, students complete the table using a calculator and plot the points on a graph. In addition they find the slope of the function at a given point.
Explore differential equations by using models representing growth and decline. Using calculus, learners will investigate exponential and logistic growth in the context of several models representing the growth or decline of a population. Most of the models have a closed-form solutions. Problems and solutions are included.
Here's a real-world lesson using a business simulation. Two business accounts are used to find slope and intercept functions. The class graphs and interprets the information to find a break even point. There are plenty of worksheets and assessments included in this lesson.
Explore the difference between stochastic and deterministic modeling through programming. First have the class write algorithms for relatively simple tasks using pseudocode. Use the Python 2.7 program app to simulate Mendel's Pea Pod experiment as an example of a stochastic process where probability and randomized variables are used and different outcomes are possible for the same inputs. Finally create a deterministic algorithm using equations and variables to simulate a dropping ball to show that the outcome is always the same for a given input. Included are examples of pseudocode and directions on how to program with the Python program.
Twelfth graders examine the Taylor Series. For this calculus lesson, 12th graders explore the representation of a function as an infinite sum of terms calculated form the values of its derivatives at a single point, hence the Taylor Series. Students use a TI-89 to explore the patterns and the command to compute the Taylor series.
In this Calculus instructional activity, students use a graphing calculator to boost their understanding of functions and their graphs as they examine the properties of curves. The forty-two page instructional activity contains one hundred problems. Answers are not provided.
Mathematicians apply the formula for line slope to determine the slope of stairs in their school. They work in small groups to take the appropriate measurements, perform the necessary calculations, and find the mean of their group slope calculations. They discuss the reasons why the slope calculations may be different.
Students explore a linear, a parabolic, and a log function. In this Algebra II/Pre-calculus lesson students investigate the graph a line, a parabola, and a log function. Students examine the three graphs as they compare and contrast the three in a problem solving context.