6.6 Intro to Logathims

Last updated about 1 year ago

25 questions

Note from the author:

OBJECTIVES & STANDARDS
Math Objectives
Explain what the purpose of a logarithm is
Convert between exponential and logarithmic functions
Use the change of base formula to evaluate logarithms
Solve exponential equations using logarithms
Common Core Math Standards
Link to all CCSS Math
CCSS.HSF.BF.B.5
CCSS.HSF.LE.A.4
Personal Finance Objectives
Use the Rule of 72
Determine the time required to meet investing goals
National Standards for Personal Financial Education
Earning Income
10d: Identify different potential sources of retirement income
Investing
2b: Compare nominal annual rates of return over time on different types of investments, including cash flows and price changes
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems

Instructions

OBJECTIVES & STANDARDS
Math Objectives
Explain what the purpose of a logarithm is
Convert between exponential and logarithmic functions
Use the change of base formula to evaluate logarithms
Solve exponential equations using logarithms
Common Core Math Standards
Link to all CCSS Math
CCSS.HSF.BF.B.5
CCSS.HSF.LE.A.4
Personal Finance Objectives
Use the Rule of 72
Determine the time required to meet investing goals
National Standards for Personal Financial Education
Earning Income
10d: Identify different potential sources of retirement income
Investing
2b: Compare nominal annual rates of return over time on different types of investments, including cash flows and price changes
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems

Intro/Warm-Up

Learn It

Application: Set Investment Goals Using Logarithms

Level 3 - Bonus

6.6 Intro to Logathims

Last updated about 1 year ago

25 questions

Note from the author:

OBJECTIVES & STANDARDS
Math Objectives
Explain what the purpose of a logarithm is
Convert between exponential and logarithmic functions
Use the change of base formula to evaluate logarithms
Solve exponential equations using logarithms
Common Core Math Standards
Link to all CCSS Math
CCSS.HSF.BF.B.5
CCSS.HSF.LE.A.4
Personal Finance Objectives
Use the Rule of 72
Determine the time required to meet investing goals
National Standards for Personal Financial Education
Earning Income
10d: Identify different potential sources of retirement income
Investing
2b: Compare nominal annual rates of return over time on different types of investments, including cash flows and price changes
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems

Instructions

OBJECTIVES & STANDARDS
Math Objectives
Explain what the purpose of a logarithm is
Convert between exponential and logarithmic functions
Use the change of base formula to evaluate logarithms
Solve exponential equations using logarithms
Common Core Math Standards
Link to all CCSS Math
CCSS.HSF.BF.B.5
CCSS.HSF.LE.A.4
Personal Finance Objectives
Use the Rule of 72
Determine the time required to meet investing goals
National Standards for Personal Financial Education
Earning Income
10d: Identify different potential sources of retirement income
Investing
2b: Compare nominal annual rates of return over time on different types of investments, including cash flows and price changes
DISTRIBUTION & PLANNING
Distribute to students
Student Activity Packet
Application Problems

Intro/Warm-Up

EXPLORE: How Long Does Your Investment Take to Mature?
Delilah makes an investment of $10,000 at 7% annual interest and wants to wait until it reaches $15,500 before withdrawing her investment.

Write an exponential equation that represents this situation where x represents years._______ 

What problems do you run into trying to solve an equation like this?

For now, estimate the amount of time it will take to reach $15,500. (We’ll revisit this later!)

Learn It

VIDEO: Introduction to Logarithms
As you saw in the intro, we sometimes need to solve for an exponent but we haven’t learned how to isolate a variable in the exponent part of an equation.  That’s where logarithms come in!  Watch this introduction to logarithms.  Then, answer the questions.

Briefly summarize what logarithms are used for.

PRACTICE: Converting Logarithms
Complete each problem by converting to the specified form.

Convert each exponential equation into logarithmic form.

_______ 
b.  
_______ 
c.  
_______ 

Convert each logarithmic equation into exponential form.

_______ 

_______ 

_______

PRACTICE: Converting to and Evaluating Logarithms
Complete each problem by converting to logarithmic form and, if necessary, solving for the variable.

Isolate each base and exponent, then convert to logarithmic form.

_______
 _______ 

_______
_______ 
_______
 _______ 

PRACTICE: Evaluating Logarithms using the Change of Base Formula
Evaluate each of the following using the change of base formula. Round to 3 decimal places.

_______ 

_______ 

_______ 

Now that we know how to use logarithms to solve for an exponent, let’s revisit Delilah’s situation from the Intro.  Recall that Delilah is investing $10,000 at 7% annual interest until her account reaches $15,500.
Use the equation that you set up in the intro and solve it to calculate how long her money must be invested before it reaches its target amount.
It would take Delilah _______ years and _______ days to reach her goal. 

Application: Set Investment Goals Using Logarithms

While diversifying her portfolio, Noelle decides to invest $12,500 into a mutual fund.  Historically, the mutual fund has yielded 7% interest annually.

Write an exponential equation to model this situation where x represents years and f(x) represents the amount of money in the mutual fund after x years._______ 

Level 3 - Bonus

FIRE stands for Financial Independence, Retire Early.  It’s a movement with the goal of individuals being extremely frugal and saving until they have enough money to retire earlier than the common age of 65.  FIRE savers use investments to help generate additional income so that they can meet their savings goals sooner and to have passive income streams after retirement.
Amos put $50,000 of his FIRE savings into an index fund that he predicts has an average annual rate of return of 9%.  He wants to generate $180,000 as a part of a larger saving strategy before his early retirement date in 15 years.

Substitute the values for Amos’ income, principal, and rate into the formula and isolate the base and exponent._______ 

6.6 Intro to Logathims

6.6 Intro to Logathims

What problems do you run into trying to solve an equation like this?

For now, estimate the amount of time it will take to reach $15,500. (We’ll revisit this later!)

Briefly summarize what logarithms are used for.

Did Amos meet his goal of generating $180,000 in interest before his early retirement in 15 years?

What problems do you run into trying to solve an equation like this?

For now, estimate the amount of time it will take to reach $15,500. (We’ll revisit this later!)

Briefly summarize what logarithms are used for.

Why might it be important for Delilah to know the exact amount of time it takes instead of an estimate?

Watch this video about the Rule of 72 then summarize what the Rule of 72 tells us.

When would it be appropriate to use the Rule of 72 instead of calculating the exact time.

Did Amos meet his goal of generating $180,000 in interest before his early retirement in 15 years?

How could Amos shift his investment strategy to meet his 15 years savings goal? Justify your response.

Why might it be important for Delilah to know the exact amount of time it takes instead of an estimate?

Watch this video about the Rule of 72 then summarize what the Rule of 72 tells us.

When would it be appropriate to use the Rule of 72 instead of calculating the exact time.

How could Amos shift his investment strategy to meet his 15 years savings goal? Justify your response.