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Part VII

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Your Money and Resources

This part of the text concentrates on numerical patterns of growth and decline in the realms of finance, resources, and biology. The unifying concept is a population, whether of dollars, barrels of oil, or tons of fish.

How much interest will your savings account earn in the next year? How much will the monthly payment be on your credit card, your car loan, or a home mortgage? How much would you need to save to pay for a child’s college education or for your retirement? What will inflation do to your savings? How much should you pay for a stock?

These are problems of daily life for which mathematics provides custom-tailored models. In Chapter 21, “Savings Models,” and Chapter 22, “Borrowing Models,” you become familiar with the mathematics and terminology of situations that you will face repeatedly in everyday life.

The financial models of these chapters apply broadly to important problems in other areas of life. Growth of a biological population is like growth of money at interest. Decay of a “population” of a radioactive substance is like depreciation of an asset or inflation of a currency. Determining how long it will be before a “population” of a nonrenewable resource, such as oil or coal, may be exhausted is like calculating how long a retirement “nest egg” will last. Managing a renewable biological resource, such as a forest or a fishery, presents problems similar to the management of a trust fund, such as the endowment of a college. In Chapter 23, “The Economics of Resources,” we explore these similarities, together with the profound effect that economic conditions can have on natural resources. Finally, you will see the surprisingly large and puzzling consequences that very small changes can produce in a physical system or biological population as a result of behavior that mathematicians call chaos.