PRACTICE: Converting to and Evaluating Logarithms
Complete each problem by converting to logarithmic form and, if necessary, solving for the variable.
6
Pitanje 7
7.
4
Pitanje 8
8.
8
Pitanje 9
9.
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
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
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
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
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.
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!)
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.
Why might it be important for Delilah to know the exact amount of time it takes instead of an estimate?
While diversifying her portfolio, Noelle decides to invest $12,500 into a mutual fund. Historically, the mutual fund has yielded 7% interest annually.
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.
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.
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.
