Population Model with Exponential Decay

The population of rabbits and foxes over a 4 month span.
t, time in months	1	2	3	4
R, number of rabbits	500	?	750	?
F, number of foxes	?	?	57	50

Population Model with Exponential Growth

Finding the size of a population of rabbits with exponential growth

Exponential Growth and Decay in Discrete Time

Explaining exponential functions in discrete time

Review for the Common Exam: MATH 151 Exam 3 Review Problems 1-7

Derivatives of exponential functions and the exponential model

Approximations and Exponentials: MATH 151 2.6 Problems 7-14

Approximation and Newton's Method, and limits and derivatives of exponential functions

Approximations and Exponentials: MATH 151 3.4 Problems 7-14

Approximation and Newton's Method, and limits and derivatives of exponential functions

Review for the Common Exam: MATH 151 Exam 3 Review Problems 1-7

Derivatives of exponential functions and the exponential model

Approximations and Exponentials: MATH 151 2.6 Problems 7-14

Approximation and Newton's Method, and limits and derivatives of exponential functions

Approximations and Exponentials: MATH 151 3.4 Problems 7-14

Approximation and Newton's Method, and limits and derivatives of exponential functions

Composition of Logarithmic and Exponential Functions

Finding the composition of two functions with exponentials and logarithms

An Equation with an Exponential Function

Solving a equation with an exponential function

An Equation with Exponential Functions of Different Bases

Solving an equation with two exponential functions with different bases

Factoring a Quadratic-Like Equation with Exponentials

Solving an equation with exponential functions by factoring

Factoring an Equation with Exponentials

Solving a equation with exponential functions by factoring

Horizontal Asymptote of an Exponential Function

Finding the horizontal asymptote of an exponential function

Horizontal Asymptote of an Exponential Function (2)

Finding the horizontal asymptote of an exponential function

Horizontal Asymptote of an Exponential Function (3)

Finding the horizontal asymptote of an exponential function

Properties of Power and Exponential Expressions Video 4

Properties of exponential growth and decay functions

Properties of Power and Exponential Expressions Video 5

Properties of the exponential function with base e

Properties of Power and Exponential Expressions Video 4

Properties of exponential growth and decay functions

Properties of Power and Exponential Expressions Video 5

Properties of the exponential function with base e

MATH 140 5.6 Exercise 1

Finding the properties of an exponential function including domain, range, end behavior, and intercepts

MATH 140 5.6 Exercise 2

Finding the properties of an exponential function including domain, range, end behavior, and intercepts

MATH 140 5.6 Exercise 3

Finding the properties of an exponential function including domain, range, end behavior, and intercepts

MATH 140 5.6 Exercise 4

Finding the domain of a function that is a fraction containing an exponential and root

MATH 140 5.6 Exercise 5

Finding the domain of a function that is a fraction containing an exponential and root

MATH 140 5.6 Exercise 6

Finding the domain of a function that is a fraction containing exponentials and a square root

MATH 140 5.6 Exercise 7

Solving an equation with exponential functions

MATH 140 5.6 Exercise 8

Solving an equation with exponential functions

MATH 140 5.6 Exercise 9

Calculating how much to invest with continuously compounded interest

MATH 140 5.7 Exercise 2

Identifying the parent function and transformations for a given graph

$MATH 140 5.7 Exercise 5$

MATH 140 5.7 Exercise 5

Identifying the parent function and transformations in order for a given function

$MATH 140 5.8 Exercise 4$

MATH 140 5.8 Exercise 4

Evaluating a logarithm inside an exponential function

$MATH 140 5.8 Exercise 9$

MATH 140 5.8 Exercise 9

Finding the domain of a function containing a logarithm, exponential, radical, and fraction

$MATH 140 5.8 Exercise 12$

MATH 140 5.8 Exercise 12

Solving an equation an exponential function

$MATH 140 5.8 Exercise 11$

MATH 140 5.8 Exercise 11

Finding the domain of a function containing a logarithm, exponential, and fraction

$MATH 140 5.8 Exercise 13$

MATH 140 5.8 Exercise 13

Solving an equation with exponential functions

$MATH 140 5.8 Exercise 14$

MATH 140 5.8 Exercise 14

Solving an equation with a logarithmic function

$MATH 140 5.8 Exercise 15$

MATH 140 5.8 Exercise 15

Solving an equation with several logarithmic functions

Limits at Infinity of a Fraction with Exponential Functions

Solving the limits approaching infinity and negative infinity with exponential functions in the numerator and denominator

Horizontal Asymptote of a Fraction with Exponential Functions

Finding the horizontal asymptotes of a function that is a fraction with exponentials in the numerator and denominator

Finding a Derivative with Exponential Functions and Logarithms

Finding the derivative a function with a power, exponential, and logarithm

Using the Product Rule with an Exponential

Finding the derivative of a function with a square root and exponential using the Product Rule

The Quotient Rule with an Exponential

Finding the derivative of a fraction with an exponential using the Quotient Rule

Using the Generalized Power Rule

Finding the derivative of a function using the Generalized Power Rule

Using the Generalized Exponential Rule

Using the Generalized Exponential Rule to find the derivative of a function

Using the Chain Rule with a Table

Using the chain rule to find derivates with some values given in a table

Using the Alternate Form of the Chain Rule

Using the alternate form of the Chain Rule to find the derivative

Using Implicit Differentiation to Find a Derivative 2

Using implicit differentiation to find the derivative of a function

Finding an Indefinite Integral

Evaluating an indefinite integral with an exponential

Finding an Indefinite Integral with a Fraction

Solving an indefinite integral by first simplifying the fraction

u-Substitution With an Exponential Function

Solving an indefinite integral with an exponential function suing u-substitution

u-Substitution With a Quotient and Exponentials

Solving an indefinite integral with exponentials in a quotient using u-substitution

Derivatives of Exponential Functions

Explaining the formulas for the derivatives of exponential functions

Derivatives of Exponential Functions Example 1

Calculating the derivative of a function with exponentials using the chain and product rule

Derivatives of Exponential Functions Example 2

Calculating a derivative of a quotient with an exponential function

Exponential Growth in Discrete Time Example

Solving a population example of exponential growth in discrete time

Recursions Example

Solving a population grown example on recurrence equations

Definition of a Semilog Plot

Explaining the logarithmic scale and a semilog plot

Semilog Plot Example 1

Using logarithms to transform an exponential function to a linear function

Semilog Plot Example 2

Writing a non-linear function to represent the line graphed on a semilog plot

Optimization Example 2

Using the second derivative to find the maximum rate of change in a word problem

WIR4 20B M150 V1

Determining properties of an exponential function

WIR4 20B M150 V2

Determining properties of an exponential function

WIR4 20B M150 V3

Determining properties of an exponential function

WIR4 20B M150 V4

Identifying the graph of an exponential function

WIR4 20B M150 V5

Solving an equation with an exponential function

WIR8 20B M150 V10

Determining properties of an exponential function

WIR4 20B M150 V17

Solving an equation with an exponential function

WIR4 20B M150 V18

Solving an equation with an exponential function

WIR4 20B M150 V19

Solving an equation with an exponential function

WIR4 20B M150 V20

Solving an equation with exponential functions by factoring

WIR4 20B M150 V25

Modeling a population size with an exponential function

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15

Review of limits and derivatives of inverse trigonometric functions

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15

Review of limits and derivatives of inverse trigonometric functions

Review for Common Exam: MATH 151 Exam 3 Review Problems 15-19

Mean Value Theorem and using derivatives to find the shape of curves

Review for Common Exam: MATH 151 Exam 3 Review Problems 25-30

Antiderivatives and physics applications

Differentiation and Applications: MATH 151 Problems 1-8

Derivatives of exponential and logarithmic functions and the exponential model

Differentiation and Applications: MATH 151 3.8 Problems 1-8

Derivatives of exponential and logarithmic functions and the exponential model

Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.2 Problems 1-6

Mean Value Theorem and properties of a graph

Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.3 Problems 1-6

Mean Value Theorem and properties of a graph

L'Hospital's Rule: MATH 151 4.4 Problem 1(a-h)

Using L'Hospital's Rule to solve limits

Riemann Sums and Definite Integrals: MATH 151 5.2 Problems 6-12

Using Reimann sums and the Fundamental Theorem of Calculus

Riemann Sums and Definite Integrals: MATH 151 5.3 Problems 6-12

Using Riemann sums and the Fundamental Theorem of Calculus

Integration by Substitution: MATH 151 5.5 Problems 13 & 14

Examples of integration by substitution

MLC WIR 20B M151 week4 #1e

Differentiating a function with an exponential function and using the Power Rule

MLC WIR 20B M151 week4 #1f

Using the Product Rule to differentiate a function

MLC WIR 20B M151 week4 #1g

Using the Quotient Rule to differentiate a function

MLC WIR 20B M151 week4 #1j

Using the Product and Quotient Rules to differentiate a function

MLC WIR 20B M151 week4 #2a

Using the Product Rule to find a first and second derivative

MLC WIR 20B M151 week4 #1mn

Using the Chain Rule to differentiate functions with exponential and trigonometric functions

MLC WIR 20B M151 week4 #2b

Using the Chain Rule to find a first and second derivative

MLC WIR 20B M151 week4 #6

Using the Chain Rule to find the pattern for a higher order derivative

MLC WIR 20B M151 week5 #1c

Finding the derivative using implicit differentiation

MLC WIR 20B M151 week5 #7a

Using logarithmic differentiation to find the derivative of a function

MLC WIR 20B M151 week5 #7b

Using logarithmic differentiation to find the derivative of a function

MLC WIR 20B M151 week5 #7c

Using logarithmic differentiation to find the derivative of a function

MLC WIR 20B M151 week6 #1ab

Using the Product and Chain Rule to find several derivatives

MLC WIR 20B M151 week6 #1cd

Using the Product, Quotient and Chain Rules to find several derivatives

MLC WIR 20B M151 week6 #1ef

Using the Quotient and Chain Rules to find several derivatives

MLC WIR 20B M151 week6 #1gh

Using the Product and Chain Rules to differentiate functions with logarithms

MLC WIR 20B M151 week6 #1ij

Differentiating functions with logarithmic and inverse trigonometric functions

MLC WIR 20B M151 week6 #1kl

Differentiating functions with inverse trigonometric functions

MLC WIR 20B M151 week6 #2a

Finding the derivative of an implicit function

MLC WIR 20B M151 week6 #2b

Finding the derivative of an implicit function

MLC WIR 20B M151 week7 #4d

Evaluating a limit using L'Hospital's Rule

MLC WIR 20B M151 week7 #4e

Evaluating a limit with an indeterminate product using L'Hospital's Rule

MLC WIR 20B M151 week7 #4f

Evaluating a limit with an indeterminant difference using L'Hospital's Rule

MLC WIR 20B M151 week7 #4g

Evaluating a limit with an indeterminate power using L'Hospital's Rule

MLC WIR 20B M151 week7 #4h

Evaluating a limit with an indeterminant power using L'Hospital's Rule

MLC WIR 20B M151 week8 #5b

Antidifferentiating twice to find a function from its second derivative

MLC WIR 20B M151 week8 #5c

Antidifferentiating twice to find a function from its second derivative

MLC WIR 20B M151 week8 #5d

Antidifferentiating to find a function from its derivative

MLC WIR 20B M151 week8 #5e

Antidifferentiating twice to find a function from its second derivative

MLC WIR 20B M151 week8 #5f

Antidifferentiating twice to find a function from its second derivative

MLC WIR 20B M151 week8 #6

Using antidifferentiation to find the height of a cliff from the impact speed of a dropped stone

MLC WIR 20B M151 week9 #8c

Evaluating a limit using L'Hospital's Rule

MLC WIR 20B M151 week9 #8d

Evaluating a limit with an indeterminant power using L'Hospital's Rule

MLC WIR 20B M151 week9 #8f

Evaluating a limit with an indeterminant product using L'Hospital's Rule

MLC WIR 20B M151 week9 #10d

Finding the antiderivative of a function and using a function value to find the constant

MLC WIR 20B M151 week10 #8c

Evaluating the limit at infinity of a fraction with exponential functions

MLC WIR 20B M151 week10 #8d

Evaluating the limit at negative infinity of a fraction with exponential functions

MLC WIR 20B M151 week10 #9c

Finding a derivative using the Chain Rule and Product Rule

MLC WIR 20B M151 week10 #19d

Using L'Hospital's Rule to solve a limit with an indeterminant power

MLC WIR 20B M151 week10 #24c

Evaluating a definite integral with an exponential and sine function

Review for the Common Exam: MATH 152 Exam 2 b Review Problems 8 & 9

Review of improper integrals and the Comparison Theorem

Review for the Common Exam: MATH 152 Exam 3 c Review Problems 13-18

Review of Taylor and Maclaurin Series and their properties

Review for the Common Exam: MATH 152 Exam 3 c Review Problems 19 & 20

Review of Taylor Polynomials and Taylor's Inequality

WIR 20B M152 V88

Finding the length of a curve given by parametric equations

WIR 20B M152 V96

Finding the area of a region defined using polar coordinates

Taylor and Maclaurin Series: MATH 152 11.10 Problems 4-10

Finding Taylor and Maclaurin Series for functions

WIR 20B M152 V83

Finding the Taylor polynomial of a function

WIR 20B M152 V70

Determining if a series is absolutely convergent, conditionally convergent, or divergent.

WIR 20B M152 V10

Finding the area of a region bounded by curves

MATH 152: Integration by Parts Exercise 1

Solving an indefinite integral with an exponential function using integration by parts

MATH 152: Integration by Parts Exercise 2

Solving a definite integral with an exponential function using integration by parts

MATH 152: Integration by Parts Exercise 8

Solving an indefinite integral with an exponential function using integration by parts

MATH 152: Integration by Parts Exercise 9

Using integration by parts twice for an integral with sine and an exponential function

WIR 20B M152 V22

Evaluating an integral using integration by parts

WIR 20B M152 V26

Evaluating an integral using integration by parts

WIR 20B M152 V1

Integrating an exponential function using u-substitution

MATH 152: u-Substitution Exercise 6

Using u-substitution on an indefinite integral with an exponential function, sine, and cosine

MATH 152: u-Substitution Exercise 8

Using u-substitution to solve an indefinite integral with an exponential function

WIR 20B M152 V43

Using the comparison test to determine if an improper integral converges or diverges

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15

Review of limits and derivatives of inverse trigonometric functions

Review for Common Exam: MATH 151 Exam 3 Review Problems 15-19

Mean Value Theorem and using derivatives to find the shape of curves

Review for Common Exam: MATH 151 Exam 3 Review Problems 25-30

Antiderivatives and physics applications

Exponentials and Hyperbolic Trigonometric Functions: MATH 171 Problems 3 & 4

Examples involving the tangent line to an exponential function and finding the derivative of hyperbolic cosine

Derivatives of Logarithmic Functions: MATH 171 Problems 7-9

Proving facts about logarithms and exponentials including the derivative of an exponential with an arbitrary base

Differentiation and Applications: MATH 151 Problems 1-8

Derivatives of exponential and logarithmic functions and the exponential model

Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.2 Problems 1-6

Mean Value Theorem and properties of a graph

Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.3 Problems 1-6

Mean Value Theorem and properties of a graph

L'Hospital's Rule: MATH 151 4.4 Problem 1(a-h)

Using L'Hospital's Rule to solve limits

Riemann Sums and Definite Integrals: MATH 151 5.2 Problems 6-12

Using Reimann sums and the Fundamental Theorem of Calculus

Riemann Sums and Definite Integrals: MATH 151 5.3 Problems 6-12

Using Riemann sums and the Fundamental Theorem of Calculus

Integration by Substitution: MATH 151 5.5 Problems 13 & 14

Examples of integration by substitution

Review for the Common Exam: MATH 152 Exam 2 b Review Problems 8 & 9

Review of improper integrals and the Comparison Theorem

Review for the Common Exam: MATH 152 Exam 3 c Review Problems 13-18

Review of Taylor and Maclaurin Series and their properties

Review for the Common Exam: MATH 152 Exam 3 c Review Problems 19 & 20

Review of Taylor Polynomials and Taylor's Inequality

Taylor and Maclaurin Series: MATH 152 11.10 Problems 4-10

Finding Taylor and Maclaurin Series for functions

WIR2 20B M251 V7

Finding the limit of a three-dimensional vector function

WIR3 20B M251 V9

Finding the partial derivatives of a function of two variables

WIR3 20B M251 V11

Finding all second-order partial derivatives of a function of two variables

WIR5 20B M251 V7

Evaluating a double integral over a given region

WIR5 20B M251 V10

Evaluating a double integral by reversing the order of integration

WIR8 20B M251 V4

Evaluating a line integral along a curve

WIR8 20B M251 V5

Evaluating a line integral along a curve in space

WIR9 20B M251 V5

Finding the curl and divergence of a three dimensional vector field

WIR10 20B M251 V4

Evaluating a surface integral of a vector field

Scalar-Valued IVP

Showing how the exponential function is the solution to an initial value problem

Statistic vs Parameter

Explanation of the difference between a statistic for a sample and a parameter for a population

$Math 140 5.4 Exercise 3$