# Exponential and logarithmic functions in carbon 14 dating rule dating someone younger

Identify the effect on the graph of replacing f(x) by f(x) k, k f(x), f(kx), **and** f(x k) for specific values of k (both positive **and** negative); find the value of k given the graphs.

Experiment with cases *and* illustrate an explanation of the effects on the graph using technology.

The **carbon**-14 decays with its half-life of 5,700 years, while the amount of **carbon**-12 remains constant in the sample.

By looking at the ratio of **carbon**-12 to **carbon**-14 in the sample **and** comparing it to the ratio in a living organism, it is possible to determine the age of a formerly living thing fairly precisely. So, if you had a fossil that had 10 percent **carbon**-14 compared to a living sample, then that fossil would be: t = [ ln (0.10) / (-0.693) ] x 5,700 years t = [ (-2.303) / (-0.693) ] x 5,700 years t = [ 3.323 ] x 5,700 years Because the half-life of **carbon**-14 is 5,700 years, it is only reliable for **dating** objects up to about 60,000 years old.

Divide both side of this equation by the initial amount of 10000. The current amount of radioactive *Carbon*-14 present in the remains of animal bones can be measured, *and* the ratio of the current amount of *Carbon*-14 to its initial amount can be used to determine age. My other lessons in this site on logarithms, *logarithmic* equations *and* relevant word problems are - WHAT IS the logarithm, - Properties of the logarithm, - Change of Base Formula for logarithms, - Solving *logarithmic* equations *and* - OVERVIEW of lessons on logarithms *logarithmic* equations *and* relevant word problems under the topic Logarithms of the section Algebra-I.

There are a variety of websites used to teach **and** reinforce how to identify **exponential** growth or decay **and** how to solve problems relating to growth **and** decay.

There is a lab provided that will help model these concepts being taught **and** computer based practice on these concepts.

Videos are provided that give a picture image of how **exponential** growth **and** decay works. For a function that models a relationship between two quantities, interpret key features of graphs **and** tables in terms of the quantities, **and** sketch graphs showing key features given a verbal description of the relationship.

Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums *and* minimums; symmetries; end behavior; *and* periodicity.* [F-IF4]36.

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