Warmup Find the inverse: 2. Find the inverse:

Slides:

Advertisements

Similar presentations

CONTINUOUSLY COMPOUNDED INTEREST FORMULA amount at the end Principal (amount at start) annual interest rate (as a decimal) time (in years)

Advertisements

Warm Up: Simplify the Expression. Then State briefly how to simplify the exponents

Essential Question: What are some of the similarities and differences between natural and common logarithms.

Logarithm Jeopardy The number e Expand/ Condense LogarithmsSolving More Solving FINAL.

LOGS EQUAL THE The inverse of an exponential function is a logarithmic function. Logarithmic Function x = log a y read: “x equals log base a of y”

Functions and Logarithms. One-to-One Functions A function f(x) is one-to-one if f(a) ≠ f(b) whenever a ≠ b. Must pass horizontal line test. Not one-to-one.

Table of Contents Solving Exponential Equations An exponential equation is an equation with a variable as part of an exponent. The following examples will.

Notes 6.6, DATE___________

2. Condense: ½ ln4 + 2 (ln6-ln2)

7.4a Notes – Evaluate Logarithms. 1. Solve for x. a. x = 2 b. c.d. x = 1 x = 0 x = -2.

Introduction Logarithms can be used to solve exponential equations that have a variable as an exponent. In compound interest problems that use the formula,

1.Simplify: 2. Simplify: 3.Simplify: 4.Simplify: 5.Simplify : 6. Simplify: Warmup

Solve the following equations for x. Show work! Round to 2 decimal places Keith has $7200 to invest for 5 years compounded continuously.

Trash-ket Ball Chapter 7 Exponents and Logarithms.

Notes – Compound Interest Formula and Pe rt With Logs Remember, the formula for compound interest is: A = P(1 + (r/n)) (n*t) with A = Amount earned, P.

Solving Exponential and Log Equations

GRAPHING EXPONENTIAL FUNCTIONS f(x) = 2 x 2 > 1 exponential growth 2 24–2 4 6 –4 y x Notice the asymptote: y = 0 Domain: All real, Range: y > 0.

Properties of Logarithms

1.Simplify: 2. Simplify: 3.Simplify: 4.Simplify: 5. Solve for x: Warmup

Daily Warm-UP Quiz 1.Expand: ln x -5 y 2 2x 2. Condense: ½ ln4 + 2 (ln6-ln2) 3. Use properties of logs to solve for x: a. log 81 = x log3 b. log x 8/64.

Warm-Up 1) Use log 3 5 = and log 3 6 = to approximate log ) Condense 7 log log 4 x + 3 log 4 y.

Solving Equations Involving Logarithmic and Exponential Functions

Simple and Compound Interest Unit 4 - Investing. Determining Simple Interest I = p * r * t Interest = Principle X Rate X Time ( in years)

LOGARITHMIC AND EXPONENTIAL EQUATIONS Intro to logarithms and solving exponential equations.

Trashketball Review Chapter 3 Exponents and Logarithms.

Compound Interest. Compound Interest (except continuous) When the bank pays interest on both the principal and the interest an account has already earned,

GCSE Mathematics Problem Solving Number Higher Tier.

Exercise Write 5% as a decimal Write 6.5% as a decimal Exercise.

Lesson 9 – 5 Exponential Equations & Inequalities

Managing your Personal Finances Unit 5 Banking Earning Simple vs

1. An account with a balance of $1000 pays 3. 65% annual

Compound Interest Making Money!!!.

COMPOUND INTEREST Since this section involves what can happen to your money, it should be of INTEREST to you!

VOCABULARY WORD DESCRIPTION Principal Interest Interest Rate

Compound Interest.

Warmup 4-25 List transformations and analyze the following

Chapter 3 Mathematics of Finance

Notes – Compound Interest Formula and Pert With Logs

Compound Interest I.. Compound Interest: A = P ( 1 + r/n)nt

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

Warm-up: THE RULE OF 72 There is a quick way to estimate the time it takes for an  investment compounded annually to double in value. This  method is called.

Change of Base.

COMPOUND INTEREST Since this section involves what can happen to your money, it should be of INTEREST to you! 

Compound Interest Making Money!!!.

3-8 PRESENT VALUE OF INVESTMENTS

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.

Time Value of Money Math

Properties of Logarithms

Unit 4: Financial Applications MAP 4C

COMPOUND INTEREST Since this section involves what can happen to your money, it should be of INTEREST to you! 

Calculating Interest Interest = the cost of ___________

COMPOUND INTEREST Since this section involves what can happen to your money, it should be of INTEREST to you! 

2-5 Compound Interest Formula

4.1/4.2 – Exponential and Logarithmic Functions

Exponential and Logarithmic Functions

Copyright © Cengage Learning. All rights reserved.

Warm Up 1) The value of a $24,500 car depreciates at a rate of 9% per year. How much is the car worth in ten years? 2) A population of 1,500 ants triples.

Exponential and Logarithmic Functions

25 = 32 Properties of Exponents Exponent Exponential Form Decimal Form

Time Value of Money Math

Jeopardy Final Jeopardy Sequences Logs Equations Inverses $100 $100

Compounded and Continuous Interest

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

C2D8 Bellwork: Fill in the table Fill in the blanks on the worksheet

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 +

8-6 Natural Logarithms.

U6D12 Have out: Bellwork: Fill in the table

Property #1 – Product Property log a (cd) =

Presentation transcript:

Warmup 5-12 1. Find the inverse: 2. Find the inverse: 3. Condense the following log expression with one log: 4. Expand the following log into multiple logs: Solve for x:

Notes – Compound Interest Formula and Pert With Logs Remember , the formula for compound interest is: A = P(1 + (r/n))(n*t) with A = Amount earned, P = Principle(amount Put in) r = interest rate n = number of times interest is compounded in a year t = time in years Steps to find t with logs: Plug in all values given for A, P, n and r into formula. Divide both sides by P. Use calculator to evaluate the (1 + (r/n)) part of formula.(DO NOT ROUND OFF) Put log with the base found in step 3 on both sides of = in front of each side. This will cancel out the base found in step 3. Exponent can then be brought down. 5. Use the calculator and change of base to calculate answer to left side of =.(Round to 2 decimal places) Set exponent(n*t) = to amount obtained in step 5 and divide both sides by number in front of t. (Round to 2 decimal places) Ex. Jeremy has $2500 to invest in an account that earns 6% interest, compounded monthly. How many years will it take him to make $4000? Ex. Joan has $4800 to invest in an account that earns 4.5% interest, compounded quarterly. How many years will it take her to earn $7200? Ex. Tim has $3500 to invest in an account compounded monthly for 6 years. What interest rate would he need to have $4900 at the end of the 6 years? Ex. Terri has $8400 to invest in an account that is compounded quarterly for 8 years. What interest rate would she need in order to double her money at the end of the 8 years?

Notes – Compound Interest Formula and Pert With Logs Remember , the formula for continuously compounded interest is: A = Pe(r*t) with A = Amount earned, P = Principle(amount Put in) r = interest rate t = time in years Steps to find r or t: Plug in all values given for A, P, and r OR t into formula. Divide both sides by P.(round to 2 decimal places) Place ln on both sides of = in front of each side. ln and e will cancel out and exponent will come down. Use calculator to find the ln of the number on the left side of the =. 5. Set exponent = to number obtained in step 4 and divide by the number next to r or t on both sides. Ex. Robert has $4200 to invest in an account earning 4% interest, compounded continuously. How many years would he need to invest the money in order to make a total of $5600? Ex. Jane has $6250 to invest in an account earning 5.5% interest, compounded continuously. How many years would she need to invest the money in order to make a total of $10000? Ex. Michael has $8400 to invest in an account compounded continuously for 6 years. What interest rate does he need to get $12600 at the end of the 6 years? Ex. Michelle has $4700 to invest in an account compounded continuously for 8 years. What interest rate does she need to double her money at the end of the 8 years?

Compound Interest Formula and Pert With Logs Practice Solve the following problems for r or t. Show work! Round all answers to 2 decimal places. 1. Dave has $2400 to invest in an account earning 5% interest, compounded monthly. How many years would he need to invest the money in order to make a total of $4200? 2. Doris has $6400 to invest in an account earning 4.5% interest, compounded quarterly. How many years would she need to invest the money in order to make a total of $8960? 3. . Chris has $5900 to invest in an account earning 6.5% interest, compounded weekly. How many years would he need to invest the money in order to double his money?

Compound Interest Formula and Pert With Logs Practice Solve the following problems for r or t. Show work! Round all answers to 2 decimal places. 4. Christine has $3600 to invest in an account compounded monthly for 4 years. What interest rate does she need to get $6480 at the end of the 4 years? 5. Keith has $4800 to invest in an account compounded quarterly for 7 years. What interest rate does he need to get $8000 at the end of the 7 years? 6. Marie has $7600 to invest in an account compounded daily for 5 years. What interest rate would she need to double her money at the end of the 5 years?

Compound Interest Formula and Pert With Logs Practice Solve the following problems for r or t. Show work! Round all answers to 2 decimal places. 7. Delores has $9600 to invest in an account earning 5.5% interest, compounded continuously. How many years would she need to invest the money in order to make a total of $14400? 8. Jeff has $7500 to invest in an account earning 4.5% interest, compounded continuously. How many years would he need to invest the money in order to make a total of $13500? 9. Francis has $8700 to invest in an account earning 6% interest, the money in order to double her money?

Compound Interest Formula and Pert With Logs Practice Solve the following problems for r or t. Show work! Round all answers to 2 decimal places. 10. Tracy has $2700 to invest in an account compounded continuously for 6 years. What interest rate does she need to get $4500 at the end of the 6 years? 11. Allen has $13200 to invest in an account compounded continuously for 8 years. What interest rate does he need to get $21120 at the end of the 8 years? Marion has $13900 to invest in an account compounded continuously for 7years. What interest rate would she need to double her money at the end of the 7 years?

Ticket out the door 5-12 Compound Interest with Logs Solve the following problems for r or t. Show work! Round all answers to 2 decimal places. 1. Terri has $4500 to invest in an account compounded monthly for 5 years. What interest rate does she need to get $6300 at the end of the 5 years? 2. Adam has $9600 to invest in an account earning 5.25% interest compounded quarterly. How long would he need to invest the money to earn $12000 at the end the investment? 3. Ellen has $15800 to invest in an account compounded continuously for 4 years. What interest rate would she need to make $18960 at the end of the 4 years? 4. Brett has $7500 to invest in an account earning 4.75% interest compounded continuously. How long would he need to invest his money to have double his original investment at the end of the term?

Warmup 12-4 1. Find the inverse: 2. Find the inverse: 3. Condense the following log expression with one log: 4. Condense the following log expression with one log: Solve for x: