Functions and Models
- Function Evaluator and Grapher
- Formula practice pop-up
- Excel Grapher (downloadable Excel workbook) For the Excel grapher to work, macros need to be enabled when you open the page.
Demand and Supply
The demand for a commodity usually goes down as its price goes up. On the other hand, the amount a manufacturer is willing to bring to the market, the supply, generally goes up as the price goes up.
The next quiz is similar to Exercise 24 in Section 1.2 of Note: You will need to enter algebraic expressions using proper graphing calculator format. Press the button to see some examples.
The demand for monorail service in the three urbynes (or districts) of Utarek, Mars can be modeled by
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million rides per day
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million rides per day.
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Use the graph to estimate the last answer accurate to 1 decimal place.
The demand and supply graphs will appear when you correctly enter them.
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Modeling Change over Time
Things all around us change with time. Thus, it is natural to think of many quantities, such as your income or the temperature in Honolulu, as functions of time. We usually use the independent variable t to denote time (in seconds, hours, days, years, etc.). If a quantity q changes with time, then we can regard q as a function of t.
In the next example (similar to Example 5 in Section 1.2 of ) we are asked to select from among several curve-fitting models for given data.
The following table shows monthly sales s(t) of Ludington's Wellington Boots (t = 0 represents January):
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s(t) |
The graph below shows a plot of these data. After successfully answering the first question below you can enter the equation of any curve to plot if you like, but you won't see anything unless graph happens to go through the window shown, like 500+50t for example.
Monthly sales of Wellington Boots
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An important analytic model of change over time comes from the compound interest formula in finance.
Compound interest
If an amount (present value) P is invested for t years at an annual rate of r, and if the interest is compounded (reinvested) m times per year, then the future value A is
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Example
If $2,000 is invested for two and a half years in a mutual fund with an annual yield of 12.6% and the earnings are reinvested each month, then P = 2,000, r = 0.126, m = 12, and t = 2.5, which gives
One for you: You invest in a mutual fund with an annual yield of and the interest is reinvested
Use the Function Evaluator and Grapher or a table in your graphing calculator to obtain the last answer. |
You now have several options:
- Try some of the questions in the true/false quiz (warning: it covers the whole of Chapter 1) by going to the "Everything" page
- Try some of the questions in the chapter review exercises (Note: they cover the whole of Chapter 1.)
- Try some of the exercises in Section 1.2 of or .
- Go on to the tutorial on linear functions by pressing "next topic" on the left.
Copyright © 2009 Stefan Waner