Derivatives of Exponential Function Teacher Resources
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Eighth graders complete problems where they use the definition of exponents to expand the squaring function of natural numbers. In this squaring natural numbers lesson plan, 8th graders also identify squares form 0 - 12 and complete a worksheet.
Students graph functions and their inverse. In this graphing functions and their inverse lesson, students plot a point and its' image. Students plot the exponential and logarithm functions. Students find the slope of the function and its inverse by taking the derivative.
In this derivatives worksheet, students sketch the graphs of four functions. They write the derivatives of eight functions. Students complete two derivative tables.
For this derivative worksheet, students find the derivative of given functions and find the equation of a tangent line to a curve. They differentiate functions and work velocity and acceleration functions. This two-page worksheet contains five multi-step problems.
In this exponential model worksheet, students read word problems, draw models, and write functions to solve the problem. This one-page worksheet contains 10 problems involving population, interest, and cell duplication.
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.
In this exponential functions worksheet, students solve 7 exponential function problems. Students find the integral and derivatives of various exponential expressions.
Students solve problems with exponential growth and decay. For this calculus lesson, students relate exponential functions to infestation and extermination. They take the derivative to find their answer.
Students explore the pattern created by a sequence or series. In this geometry lesson plan, students relate the spread of a virus to the growth of exponential functions. They collect data as they analyze the sequence created by the growth.
For this 2-day lesson focused on exponents, middle schoolers will cross the curriculum by engaging in science, history and language arts activities. Exponential growth will be explored using grains of rice on a chess board. Exponential power, as well as the power of one, will be connected to a historical event as a way for the class to make connections to real-world events.
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.
Twelfth graders examine multiple aspects of statistics. In this mathematical reasoning lesson, 12th graders solve problems on probability, logarithms, exponential relationships and transforming rectilinear shapes. This resource contains several lessons which include extensions, vocabulary, and related activities.
Students explore a variety of relationships using pennies, pressure, temperature, light and pendulums to determine the algebraic equation that best represents the pattern modeled by the variables involved in each situation.
In this continuous probability distribution worksheet, students identify discrete and continuous distributions. They calculate the linear combination of the independent normal random variable and determine probabilities using exponential distribution. This 20 page worksheet contains approximately 100 problems. Explanations and examples are provided throughout the document.
Students review correct classroom procedures. In this algebra lesson, students are taught how to identify exponential graphs and identify the assyptotes and write an exponential formula.
Twelfth graders review concepts of logarithms for their test. In this calculus lesson, 12th graders review inverse function, limits, deratives and solving logs equations. They review the chain rule and domain and range of inverse logs.
In this calculus activity, students use integration to solve word problems they differentiate between integration and anti derivatives, and between definite and indefinite integrals. There are 3 questions with an answer key.
Investigate logistic functions in a world population setting. High schoolers will create a scatter plot of the world population from 1950 to 2050 to find a logistic function to model the data. They then discuss the end behavior of their logistic model. Graphing calculators are needed.
High schoolers investigate logistic models by making a scatter plot of internet phone users over 5 years. They find a logistic model that fits their data and then discuss what the instantaneous rate of change means in the context of the problem. Very relevant and applicable!
Students solve the mystery of dead Mr. Potato Head using physics and algebra. They discuss Newton's Law of cooling as it applies to the mystery scenario involving a cooling baked potato as the "victim". They manipulate algebraic equations to find the time of death.