Author: Dr Dave

Piecewise Functions and Taxes

A terrific example of piecewise functions is our graduated income tax system. In that system, the more you make…the higher percentage you pay. However, you DO NOT pay the higher percentage on all of your income. In the two FAQ’s below,we take a look how all of this works.

This FAQ shows how to take a tax table from the Arizona tax forms and convert it into a piecewise function.

In this FAQ we incorporate the idea that the amount you are taxed depends on the tax bracket you fit in.

This topics comes from Section 1 of Chapter 10 in Applied Calculus and is used in Section 5 of the same chapter.

Present Value…A Moving Target

In many investment problems, you are given an amount of money and asked what will it accumulate to in a certain amount of time at some interest rate. Essentially, these problems are asking you to find the future value of the amount of money. Depending on how that money accumulates, you might use one of several different formulas.

The MathFAQ below looks at how you calculate present value in the context of different type of interest.

Goto the MathFAQ >.

Real Life Points of Inflection

Points of Inflection are locations on a graph where the concavity changes. In the case of the graph above, we can see that the graph is concave down to the left of the inflection point and concave down to the right of the infection point. We can use the second derivative to find such points as in the MathFAQ below.

What is the significance of this point? On both sides of the inflection point, the graph is increasing. This means that as the number of connections increased, so did the revenue from those connections. However, on the left side of the inflection point, the increases in revenue due to increasing connections is getting smaller and smaller. On the right side of the point of inflection, increasing the connections results in larger and larger increases in revenue.