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# Continuity, Trends and Forecasting

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1) What is a discontinuity? How are discontinuities found? Which types of graphs are continuous?

3) If Bob starts off with a salary of \$50,000 and earned \$1000 a year for his salary, give the equation of his salary, S, for year t. Use this equation to find the year in which he would be earning \$56,400. Show all your work using the equation.

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#### Solution Preview

From mathworld.com the definition of continuous is:

A general mathematical property obeyed by mathematical objects in which all elements are within a neighborhood of nearby points. The continuous maps between topological spaces form a category. The designation "continuous" is sometimes used to indicate membership in this category.

This means that a function f(x) is continuous if its value approach f(a) as x approaches a

Check out:
http://sosmath.com/calculus/limcon/limcon05/limcon05.html

In functions, we have three types of discontinuity:

1. The function is not defined at a certain point.

for example, look at the function:

{2 x<0
f(x) ={
{2 x>0

As you can see, the function has a value everywhere except at x=0 in which we don't know what ...

#### Solution Summary

Discontinuities, trends and forecasting are investigated in the following posting.

\$2.49