5.5 Bases Other Than e and Applications

Slides:

Advertisements

Similar presentations

Exponential Growth and Decay

Advertisements

6.2 Growth and Decay Law of Exponential Growth and Decay C = initial value k = constant of proportionality if k > 0, exponential growth occurs if k < 0,

Diff EQs 6.6. Common Problems: Exponential Growth and Decay Compound Interest Radiation and half-life Newton’s law of cooling Other fun topics.

Warm-Up Solve for x in each equation. a) 3 x = b) log 2 x = –4 c) 5 x = 30.

Objective: To identify and solve exponential functions.

Logarithmic, Exponential, and Other Transcendental Functions Copyright © Cengage Learning. All rights reserved.

INTRODUCTORY MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences  2007 Pearson Education Asia Chapter 4 Exponential and Logarithmic.

Lesson 9-4 Exponential Growth and Decay. Generally these take on the form Where p 0 is the initial condition at time t= 0 population shrinking  decay.

Objective: To use exponential and logarithmic functions to solve problems.

Applications and Models: Growth and Decay

 If you deposit $10,000 into an account earning 3.5% interest compounded quarterly;  How much will you have in the account after 15 years?  How much.

One model for the growth of a population is based on the assumption that the population grows at a rate proportional to the size of the population. That.

Section 4.2 Logarithms and Exponential Models. The half-life of a substance is the amount of time it takes for a decreasing exponential function to decay.

Notes Over 7 – 7 Solve for the indicated variable.

Differential Equations: Growth and Decay Calculus 5.6.

Aim: Other Bases Course: Calculus Do Now: Aim: How do we differentiate and integrate the exponential function with other bases? Find the extrema for w/o.

Section 6 Chapter Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Exponential and Logarithmic Equations; Further Applications.

Exponential Growth and Decay. Objectives Solve applications problems involving exponential growth and decay.

7.3B Applications of Solving Exponential Equations

6.2 Growth and Decay Obj: set up and solve growth and decay problems.

Chapter 6 Integration Section 3 Differential Equations; Growth and Decay.

6.4 Exponential Growth and Decay Law of Exponential Change Continuously Compounded Interest Radioactivity Newton’s Law of Cooling Resistance Proportional.

Logarithmic, Exponential, and Other Transcendental Functions 5 Copyright © Cengage Learning. All rights reserved.

E XPONENTIAL W ORD P ROBLEMS Unit 3 Day 5. D O -N OW.

 Suppose you deposit $800 in an account that pays 6.3% annual interest. How much will you have 8 years later if the interest is (a) compounded.

Calculus 5-R Unit 5 Logarithmic, Exponential and Other Transcendental Functions Review Problems.

EXAMPLE 5 Find the balance in an account

MAT 142 Lecture Video Series

Aim: How do we solve verbal problems leading to

Differential Equations

Applications of Exponential Functions

Compound Interest.

7-4 Exponential Growth and Decay

Exponential Functions, Growth and Decay

Happy Friday Eve! Do the following: Warm-up  Do on whiteboard HW #6:

Chapter 3 Mathematics of Finance

8-8 Exponential Growth and Decay

Pass up your homework and clear your desk for the QUIZ

Exponential and Logarithmic Equations

Chapter 4 Exponential and Logarithmic Functions.

Warm Up If you deposit $10,000 into an account earning 3.5% interest compounded quarterly; How much will you have in the account after 15 years? How.

Examples Compound Interest

Review Problems Chapter 5.1 – 5.7

Exponential Growth and Decay

6.1 Exponential Growth and Decay Functions

Do Now If you did not finish it yesterday, put your worksheet into the basket In the standard form y = a•bx, what does each variable represent? If Ms.

Exponential Functions

What do all of these have to do with Calculus?!?!?

Janie’s bank pays 2.8% annual interest compounded continuously on savings accounts. She placed $3000 in the account. How much money will be in Janie’s.

Examples Compound Interest

Sam opened a savings account that compounds interest at a rate of 3% annually. Let P be the initial amount Sam deposited and let t be the number of years.

3.5 Exponential Growth & Decay

Compound Interest.

Imagine you have a baseball card that is worth exactly $1

7.5b - Applications of Logarithms

Exponential Functions and Their Graphs

Section 4.8: Exponential Growth & Decay

Exponential and Logarithmic Models

HOW TO MAKE MONEY WITHOUT DOING ANY WORK

Section 4.8: Exponential Growth & Decay

Homework: Handout Aim: How do we solve verbal problems leading to

Further Applications and Modeling with

6.1 Exponential Growth and Decay Functions

5.4 Applications of Exponential Functions

Logarithmic, Exponential, and Other Transcendental Functions

Homework: Handout Aim: How do we solve verbal problems leading to

5.2 Growth and Decay Law of Exponential Growth and Decay

5.5 Bases Other than e and Applications (Part 2)

Presentation transcript:

5.5 Bases Other Than e and Applications

Bases Other Than e

Radioactive Half-Life Model The half-life of carbon-14 is about 5715 years. A sample contains 1 gram of carbo-14. How much will be present in 10000 years?

Bases Other Than e Solve for x in each equation.

Differentiating Functions to Other Bases Find the derivative of each function.

Integrals for Bases Other than e

Comparing Variables and Constants

Compound Interest Formulas

Comparing Continuous and Quarterly Compounding A deposit of $2500 is made in an account that pays an annual interest rate of 5%. Find the balance in the account at the end of 5 years if the interest is compounded a) quarterly, b) monthly, and c) continuously.

Bacterial Culture Growth A bacterial culture is growing according to the logistic growth function where y is the weight of the culture in grams and t is the time in hours. Find the weight of the culture after a) 0 hours, b) 1 hour, c) 10 hours. d) What is the limit as t approaches infinity.