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

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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

SLIDE 1

Alert!

AIM (9.6) : How do we use logarithms to determine the time of compounding interest?

Take two minutes to get your Notebooks, Calculators, & Student Orgzniers before we begin today's lesson.

A l e r t !

SLIDE 2

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

SLIDE 3

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

SLIDE 4

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.

SLIDE 5

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

SLIDE 6

How much money would you need to deposit today at 6% annual interest compounded quarterly to have $10,000 in the account after 5 years? 1) 2) 3) 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 puts some money in a bank account that compounds continuously at an annual interest rate of 7%. If he's 18 years

ld now, how much will have to put in today to achieve his

goal.

3 Correct 0 1 Correct 2 Correct

HOMEWORK REVIEW

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

SLIDE 7

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

SLIDE 8

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

SLIDE 9

HOMEWORK REVIEW

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

SLIDE 10

HOMEWORK REVIEW

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

SLIDE 11

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

SLIDE 12

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

SLIDE 13

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

SLIDE 14

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

SLIDE 15

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

SLIDE 16

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

SLIDE 17

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

SLIDE 18

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

SLIDE 19

Classwork Time!

Complete Classwork independently
Check your answers with a partner.
If you get stuck, signal red.

All even # questions

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

SLIDE 20

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

SLIDE 21

Classwork Answers

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

SLIDE 22

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

SLIDE 23

Classwork Answers

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

SLIDE 24

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?

Take two minutes to get your Notebooks, Calculators, & Student Orgzniers before we begin today's lesson.

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?

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?

DoNow Begins!

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.

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.

goal.

HOMEWORK REVIEW

HOMEWORK REVIEW

4.Choice D 5. a) b) c) 6. a) b) c)

HOMEWORK REVIEW Choice D models decay because the base, 0.98, is between 0 and 1.

HOMEWORK REVIEW

HOMEWORK REVIEW

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.

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

Practice solving using logs

tenth:

Practice solving using logs

What's different here?

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:

How do we use logarithms in compounding interest?

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.

How do we use logarithms to solve problems involving compounding interest?

Classwork Time!

All even # questions

Classwork Answers

2) 4) 6) 8) 10) 12)

Classwork Answers

Classwork Answers

Classwork Answers

Get a head start on your homework!

Tuesdays 207A & Fridays

AIM (9.6) : How do we use logarithms to determine the time of compounding interest?

Take two minutes to get your Notebooks, Calculators, & Student Orgzniers before we begin today's lesson.

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?

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?

Do­Now Begins!

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.

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.

goal.

HOMEWORK REVIEW

HOMEWORK REVIEW

4.Choice D 5. a) b) c) 6. a) b) c)

HOMEWORK REVIEW Choice D models decay because the base, 0.98, is between 0 and 1.

HOMEWORK REVIEW

HOMEWORK REVIEW

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.

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

Practice solving using logs

tenth:

Practice solving using logs

What's different here?

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:

How do we use logarithms in compounding interest?

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.

How do we use logarithms to solve problems involving compounding interest?

Classwork Time!

All even # questions

Classwork Answers

2) 4) 6) 8) 10) 12)

Classwork Answers

Classwork Answers

Classwork Answers

Get a head start on your homework!

Tuesdays 207A & Fridays

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?

DoNow Begins!

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.

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.

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.