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The half-life of Potassium 40 is 1.3 billion years. A rock has been estimated to be 4 billion years old. What percent of the original Potassium 40 in the rock remains?

$$11.85 \%$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

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Lectures

01:46

If a rock was determined t…

00:48

A paleontologist estimates…

02:18

03:51

Potassium-40 decays to arg…

01:31

Potassium- 40 decays to ${…

04:39

Potassium- 40 has a half-l…

03:13

A Potassium-40 decays to $…

Given that the potassium half life is 1.3 billion years and that Iraq has been found an estimated to be about 44 billion years old. What percent of the original potassium is likely to be remaining in that rock? So we're going to be using the formulas bubbled in green. It's fairly straightforward that the ending amount is equal to the beginning amount divided by two to the power of N. Where N. Is the elapsed time divided by the half life. So that's what we need to start by finding. So we know that about four billion years has elapsed because that's how old this rock is. And we also know that the half life is about 1.3 billion years. This tells us that N. is equal to 3.0769. That means just over three half lives have passed over this course of four billion years. Oh I don't know how to define this percent of the original potassium remaining. That's where we're going to bump to this ending amount formula. So for that ending amount, I'm just going to call that a Just then equal to our beginning amount. We're working with percentages here. That's what it's asking. So assuming that we started with 100% of this potassium in the rock, Then divide that by two to the power of end that we just found 3.0769, Then 100 divided by that will give us 11.8 5%. So it's just saying that about 11.85% of that original potassium is still remaining in this four billion year old rock.

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