## Tutorial: Functions and models

This tutorial: Part B: Demand, supply and time-change models

(This topic is also in Section 1.2 in *Finite Mathematics and Applied Calculus*) #[I don't like this new tutorial. Take me back to the older tutorial!][No me gusta este nueve tutorial. ¡Regresame al tutorial más viejo!]#

### Resources

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. Sometimes, it may be difficult or even impossible to find the equilibrium point algebraically as you did in the above question, and you may want to estimate it graphically instead.

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 %%comboref we are asked to select from among several curve-fitting models for given data.
Compound interest

A fundamental example of a time-change model in financial mathematics is that of compound interest.
#[Compound interest formula][Fórmula de interés compuesto]#

The future value of an investment of $P$ dollars earning interest at an annual rate of $r$ compounded $n$ times per year for $t$ years is
$\displaystyle A(t) = P\left(1 + \frac{r}{n}\right)^{nt}. \quad$ \t An exponential function of $t$

**A special case:**Interest compounded once a year The future value of an investment of $P$ dollars earning interest at an annual rate of $r$ compounded once per year for $t$ years is

$\displaystyle A(t) = P\left(1 + r\right)^{t}. \qquad$ \t Set $m = 1$ in above formula.

**#[Your Turn][Tu turno]#**

Now try the exercises in Section 1.2 in

*Finite Mathematics and Applied Calculus*. or move ahead to the next tutorial by pressing "Next tutorial" on the sidebar.
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Copyright © 2019, 2023 Stefan Waner and Steven R. Costenoble

*October 2023*Copyright © 2019, 2023 Stefan Waner and Steven R. Costenoble