Continually Compounded. Definition/Formula The natural logarithmic function can be used to solve an equation of the form for the exponent t in order to.

Slides:

Advertisements

Similar presentations

Models of Exponential and Log Functions Properties of Logarithms Solving Exponential and Log Functions Exponential Growth and Decay

Advertisements

Logarithmic Functions

7.7 Day 1 Notes Base e and Natural Logarithms

Exponential and Logarithmic Equations. Exponential Equations Exponential Equation: an equation where the exponent includes a variable. To solve, you take.

Exponential Growth & Decay Modeling Data Objectives –Model exponential growth & decay –Model data with exponential & logarithmic functions. 1.

Logarithmic Functions. Objectives To write exponential equations in logarithmic form. To use properties of logarithms to expand and condense logarithmic.

Exponential Equations Like Bases. Warm Up  The following quadratic equation has exactly one solution for x. Find the value of k. Explore more than one.

Applications and Models: Growth and Decay

#1. #2 #3 Graph by hand. #4 #5 If $5000 is invested at 9% interest, find the amount after three years if the interest is compounded (a) monthly.

6.6 The Natural Base, e Objectives: Evaluate natural exponential and natural logarithmic functions.

6.6 The Natural Base, e Objectives: Evaluate natural exponential and

Aim: How do we solve exponential equations using common or natural logarithms? Do Now: 1. Solve for x: 3 x = Solve for x: 4 x = 8 3. Solve for x:

3.4 Solving Exponential and Logarithmic Equations.

6.6 The Natural Base, e Objectives: Evaluate natural exponential and natural logarithmic functions.

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

3.2 Logarithmic Functions 2015 Digital Lesson. 3.1 Warm-up Mr. Smith deposited $6,500 in an account that pays the account pays 4.5% interest, compounded.

5.7 – Exponential Equations; Changing Bases

Find the amount after 7 years if $100 is invested at an interest rate of 13% per year if it is a. compounded annually b. compounded quarterly.

Elimination Method Day 2 Today’s Objective: I can solve a system using elimination.

ACTIVITY 39 Exponential and Logarithmic (Section 5.4, pp ) Equations.

How do we solve exponential and logarithmic equations and equalities?

3.2 Logarithmic Functions. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Intro Solving for an answer Solving for a baseSolving.

Solving Equations Exponential Logarithmic Applications.

4.4 Exponential and Logarithmic Equations. Solve: 2 x = 7 3 x+3 = 5.

3.2 Logarithmic Functions. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Intro Solving for an answer Solving for a baseSolving.

Interest Applications - To solve problems involving interest.

Exponential Functions You start a new job at age 22. If you invest $125 in a retirement plan each month, your company will invest another $125. The investment.

3.5 Exponential and Logarithmic Models n compoundings per yearContinuous Compounding.

Table of Contents 5. Section 5.8 Exponential Growth and Decay.

 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.

Bellwork Solve. 1) Find the final amount of a $800 investment after 5 years at 3.7% interest compounded monthly. Tell whether each function represents.

GCSE Mathematics Problem Solving Number Higher Tier.

4 Exponential and Logarithmic Functions.

Applications and Models: Growth and Decay; and Compound Interest

Aim: How do we solve verbal problems leading to

Find the solution of the exponential equation, correct to four decimal places. e x =

Unit 3– Exponentials and Logarithms Review Problems

Exponential Equations

CHAPTER 5: Exponential and Logarithmic Functions

Exponential and Logarithmic Equations

Exponential and Logarithmic Equations

Inverse, Exponential, and Logarithmic Functions

Chapter 5: Inverse, Exponential, and Logarithmic Functions

Solving Logarithmic Equations

Applications and Models: Growth and Decay; and Compound Interest

3.2 Logarithmic Functions

6.6 The Natural Base, e Objectives: Evaluate natural exponential and

3-8 PRESENT VALUE OF INVESTMENTS

Logarithmic Functions

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.

Exponential Equations Applications.

5.6 Applications and Models: Growth and Decay; and Compound Interest

4.1/4.2 – Exponential and Logarithmic Functions

Which Equation? $1000 is invested in an account that accrues 12% annual interest. A radioactive isotope has a half-life of 12 hours. $500 is deposited.

CHAPTER 5: Exponential and Logarithmic Functions

Inverse, Exponential and Logarithmic Functions

Chapter 5.2 Vocab.

Logarithmic Functions

Warm-Up Evaluate log x for each value. x = 10 x = 0.1 x = -10 x = 1

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

Mathematical Explorations

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

Logarithmic Functions

Rule of 72 The answers can be easily discovered by knowing the Rule of 72 The time it will take an investment (or debt) to double in value at a given interest.

Warmup Solve 2x – 4 = 14. Round to the nearest ten-thousandth. Show all logarithmic work.

Compound Interest If a principal P is invested at an interest rate r for a period of t years, then the amount A of the investment is given by A = P(1 +

example 3 Carbon-14 Dating

Jeopardy Choose a category. Click to begin..

Example 7 Investment The future value of $3000 invested for 3 years at rate r, compounded annually, is given by What interest rate will give a future value.

Presentation transcript:

Continually Compounded

Definition/Formula The natural logarithmic function can be used to solve an equation of the form for the exponent t in order to find the time it takes for an investment that is compounded continuously to reach a specific amount.

Example How long does it take for an investment to double at an annual amount of 8.5% compounded continuously?

Example How long does it take an investment to double at an annual rate of 7.5% compounded continuously?

Example Find the amount, A, for an investment of $1000 at an annual rate of 4% for 10 years.

Example How long will it take to double your money if you deposit $1200 at an annual rate of 6.9% compounded continuously?

Radioactive Decay The function represents the decay of carbon-14, where:

Example A piece of charcoal from an ancient campsite is found in an archaeological dig. It contains 9% of its original amount of carbon-14. Estimate the age of the charcoal.

Assignment Complete WS 4 #13-23