The Purplemath Forums

by **afew** on Tue Apr 21, 2009 2:31 am

The half-life of potassium-40 is approx. 1.31 billions years. analysis of some rocks around some dinosaur bones indicated that 94.5% of the original amount of potassium-40 was still present. Estimate the age of the bones of the dinosaur.

I haven't a clue how to approach this. im assuming your supposed to use the formula A=Aoe^kt but i have no idea where to input any of the information. please help :confused:

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by **stapel_eliz** on Tue Apr 21, 2009 12:33 pm

afew wrote:The half-life of potassium-40 is approx. 1.31 billions years. analysis of some rocks around some dinosaur bones indicated that 94.5% of the original amount of potassium-40 was still present. Estimate the age of the bones of the dinosaur.

One customarily uses the "continously-compounded" formula for this sort of exercise.

. . . . . $A\, =\, Pe^{rt}$

You are given that, in t = 1.31 (where "t" is measured in "billions of years"), A = (1/2)P. That is:

. . . . . $\frac{P}{2}\, =\, Pe^{1.31r}$

. . . . . $\frac{1}{2}\, =\, e^{1.31r}$

Solve the exponential equation for the value of the decay constant "r".

Now that you have the value of "r", you can do the second part of the exercise: finding the age, given an amount. Whatever the initial amount P was, you now have A = 0.945P left. So plug these into the equation, and solve for the time "t". :wink:

If you get stuck, please reply showing how far you have gotten. Thank you!