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Contrast Asymptotes and a Real-Life Exponential Function

One of the archaeologists you interviewed for your article is graphing asymptotes to illustrate the data generated through carbon dating the half-life of fossil specimens. Help him with his work by solving these problems:
1. Explain and contrast the types of asymptotes considered for rational functions.
2. Browse through some newspapers or magazines and find a situation that fits an exponential function . Explain why that data or situation fits an exponential function.

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(1) Rational functions exhibit three types of asymptotes:

* Vertical asymptotes. These are vertical lines near which the function f(x) becomes infinite. If the denominator of a rational function has more factors of (x - a) than the numerator, then the rational function will have a vertical asymptote at x = a.

* Horizontal Asymptotes. A horizontal asymptote is a line y = c such that the values of f(x) get increasingly close to the ...

Solution Summary

Asymptotes and exponential functions are discussed. The solution is detailed and well presented in about 320 words.