Using Mathematical Models to Make Decisions Module Overview

Mathematics is about the patterns that arise in the world about us. Good mathematical models are often versatile and flexible, and the models of this unit apply to problems of life. Growth of money at interest is like growth of biological populations. Inflation of a currency or depreciation of an assets is like decay of radioactive substance.

How much interest will your savings account earn in the next year? How much will the payment be on your credit card, your car loan or a home mortgage? What will inflation do to your savings? How should you pay for your stock? These are daily life problems for which mathematics provide custom-tailored models.

In this unit, you will consider models that change over time: bank accounts, the amount due on a loan, temperature effects and the size of a population. You will see how mathematics can be applied to your life in interesting, enjoyable, and meaningful ways. You will become familiar with the mathematics and terminology of financial situations that you will face repeatedly.

Essential Questions

How much interest will your savings account earn in the next year?
How much will the payment be on your credit card, your car loan or a home mortgage?
What might we mean by bivariate data? How long will it take to save $2000?
How much money do you think you will need for retirement?
What are some ways you, your friends, or your family have been paid for a job?
What is the difference between simple interest and compound interest?
How does the length of an investment affect the amount of money earned?
What will $1000 be worth in 5 years?
What are the main factors in determining the present or future value of an investment?
How much money do you think you will need for retirement?
Suppose you bought 100 shares of stock 10 or 20 years ago. What would it be worth today?
What kind of credit offers have you seen in advertisements and mailings?
Why is buying a car a losing investment?
How can money earned be thought of as a sequence of values?
How do we determine the rate of change in an earnings model?
Why do you think the prices of goods change over time?
Will the temperature of a hot cup of coffee change at a constant rate?
Are there patterns observed in functions without a constant rate of change?
What types of models are used for investigating events involving time?
What significant differences in time/seasons exist between the Southern and Northern Hemisphere?
How do hurricanes affect the weather of Florida?
What mathematics can be observed in a Ferris Wheel?
What do you think the rebound percentage is for a tennis ball? A basketball? A racquetball?
When taking medication, is it important to take the same amount each day?

Key Terms

The following key terms will help you understand the content in this module.

2 dimensional representation (2D) - a figure that has 2 dimensions represented in a flat plane by length and width
3 dimensional representation (3D) - a figure that has 3 dimensions represented by length, width, and height
annuity - an investment with a sequence of equal payments made at equal time periods.
bonds - an investment in which a commitment from a company to pay the price an investor pays for the bond at the time it was purchased along with interest payments at a given rate.
bivariate data - data that involves two different variables whose values can change
compound interest - interest computed on the original principal as well as on accumulated interest.
compounding period - the period of time between two interest payments
continuous data - data that takes on any measured value and can include decimals or fractions
discrete data - data that is measured by only whole positive units or data that can be placed into distinct categories
exponential function - a function with a constant multiplier
function rule - defines a term in a sequence using the term number and is based on an input-output model
geometric sequence - a pattern of numbers that has a constant ratio between consecutive terms
installment loans- a loan that you pay off with payments in some time period
linear function - a function with a constant rate of change
periodic function - functions that repeat over and over, or cycle on a specific period
recursive rule - defines a term in a sequence using the previous term and is based on an iterative process
simple interest - only calculated on the principal.
step function - special piecewise function with a series of segments
stocks - an investment based on shares of ownership in a company.

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