AIM (9.6) : How do we use logarithms to determine the time of - PDF document

AIM (9.6) : How do we use logarithms to determine the time of compounding interest? Alert! Take two minutes to get your Notebooks, Calculators, & Student Orgzniers before we begin today's lesson. A l e r t !

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 Exit Ticket as Do­Now On Post­It How money would you need to deposit into an account that earns 8% interest compounded continuously in order to have $50,000 after 10 years?

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 Exit Ticket How money would you need to deposit into an account that earns 8% interest compounded continuously in order to have $50,000 after 10 years?

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 Do­Now Begins! Mr. Lo just sold his arcade for $205,000. Assuming an exponential growth rate of 15% a year compounded semi­annually, and that Mr. Lo bought his arcade around 10 years ago, determine how much Mr. Lo originally bought the arcade for. Round your answer to the nearest whole number.

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 Mr. Lo just sold his arcade for $205,000. Assuming an exponential growth rate of 15% a year compounded semi­annually, and that Mr. Lo bought his arcade around 10 years ago, determine how much Mr. Lo originally bought the arcade for. Round your answer to the nearest whole number.

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 HOMEWORK REVIEW How much money would you need to deposit today at 6% 1) annual interest compounded quarterly to have $10,000 in the account after 5 years? 2) What principal will amount to $7,500 if invested at 4% interest compounded monthly for 8 years? Roberto wants to have $1,000,000 by the time he is 65. He 3) puts some money in a bank account that compounds continuously at an annual interest rate of 7%. If he's 18 years old now, how much will have to put in today to achieve his goal. 0 ­ 1 2 3 Correct Correct Correct

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 HOMEWORK REVIEW What do we want to go over as a class? 4.Choice D 5. a) b) c) 6. a) b) c)

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 HOMEWORK REVIEW Choice D models decay because the base, 0.98, is between 0 and 1.

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 HOMEWORK REVIEW

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 HOMEWORK REVIEW

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 What are Logarithms? Logarithms are inverses of exponential functions. Simply, they are used to solve for an unknown exponent with a base. In exponential situations (like compound interest), logarithms are used to find the time when all other parts are known. What is happening below?

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 How do logarithms work? There are many rules for logarithms, but for the purpose of compounding interest, we only need to know this one rule: To remember: The exponent was brought down because it was hit with a log log( ) a X

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 Practice solving using logs Ex. 1 Solve for the variable, round to nearest tenth:

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 Practice solving using logs Ex. 2 Solve for the variable:

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 What's different here? Ex. 3 Solve for the variable, round to nearest hundredth: There's a special kind of logarithm called the "Natural" logarithm, Ln. This is used specifically for Euler's number because of its special relationship: *Whenever you are solving and see Euler's number, e, use the natural logarithm, Ln.

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 How do we use logarithms in compounding interest? Ex. 4 Mr. Lo purchased an arcade some years ago for $50,000, and just sold it today for $205,000. Assuming an exponential growth rate of 15% a year compounded semi­annually, determine how long ago the arcade was purchased. Round your answer to the nearest year.

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 Ex. 5 Adonis purchased a house in the Bronx for $305,000 with his hard earned cash! But Adonis is not about that Bronx life and wants to move down to Miami. If Adonis wants to sell his house for $700,000 and the value of his house is growing at 20% a year compounded quarterly, determine how long Adonis must wait until he can sell his Bronx home. Round your answer to the nearest year.

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 How do we use logarithms to solve problems involving compounding interest?

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 Classwork Time! All even # questions • Complete Classwork independently • Check your answers with a partner. • If you get stuck, signal red .

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 Classwork Answers Do we need to go over any questions? 2) 4) 6) 8) 10) 12)

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 Classwork Answers

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 Classwork Answers Notice how I left 100/63 as a fraction instead of evaluating it. If you get irrational numbers (or repeating decimals) during calculations, leave the expression as it is until the last step. This avoids any rounding errors which may deduct a point off on the Regents exam.

Aim 9.6: How do we use logarithms to determine the time of compounding interest? HW: Complete worksheet 9.6 Classwork Answers

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