Derivatives of Exponential Function Teacher Resources
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Differentiating Special Functions
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.
Pre-calculus Unit 3 Test 2
Students will solve exponential function problems, graph exponential functions, find the value of logarithms, determine future value, and compound interest. In this Pre-calculus lesson, students will use the properties of logs to solve test problems.
Biological Models with Differential Equations
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.
Why Are Hot Things Red?
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.
In this precalc lesson, students write out definitions, identify functions, solve integrals and derivatives and graph trig functions as they relate to angles. This is a final exam for precalculus. There are 80 questions on this exam.
Shedding Light on the Subject: Function Models of Light Decay
Students develop and analyze exponential models for the behavior of light passing through water.
Stochastic and Deterministic Modeling
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.
Derivatives of Inverse Functions
In this derivatives worksheet, students use the chain rule to show equalities between functions. They read a tutorial that guides them through the process of using the chain rule to find derivatives. This worksheet includes five short answer problems.
Sudoku Puzzle: Logs and Exponentials
In this logarithms and exponential worksheet, students solve 29 multiple choice problems. Students use their answers to solve a sudoku puzzle.
Movement with Functions
Students create functions from graphs. In this movement with functions lesson, students use motion detectors and create graphs from the movement. Afterward, they describe graphs and write equations for the graphs.
Worksheet 26 - Functions & Logarithms
In this function and logarithms worksheet, students find the domain and range of functions, use the properties of logs to solve equations. This one-page worksheet contains nine multi-step problems.
Linear Functions: Are You Ready for the Real World?
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.
Polynomial Approximations--An Introduction to the Taylor Series
Twelfth graders examine the Taylor Series. In 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.
Linear and Quadratic Approximations
Students explore a linear, a parabolic, and a log function. In this Algebra II/Pre-calculus lesson plan 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.
Properties of Curves
In this Calculus worksheet, 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 worksheet contains one hundred problems. Answers are not provided.
Off to College
High schoolers investigate linear, quadratic and exponential equations using the TI calculator. They identify relation and functions using ordered pairs, graph the data, analyze the data, and relate it to real-world situations.
Track the Trends: Predict the Future
Learners choose a subject of interest and collect related statistical information. They use a graphing calculator to derive the equation for curve of best fit for the data and then predict future trends.
Complex Analysis: Complex Exponents
In this complex exponents instructional activity, students determine the domain of analyticity of a function. This six-page instructional activity contains ten problems.
Exploration 3: Introduction to Definite Integrals
In this integral worksheet, students estimate the definite integral and find the derivative of functions. They graph functions and determine the range of the velocity. This three-page worksheet contains approximately 40 problems.
Section 7.4 Practice: The Exponential Function
In this exponential functions learning exercise, students solve 7 exponential function problems. Students find the integral and derivatives of various exponential expressions.