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.