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If radioactive Carbon 14 has a half-life of approximately 5745 years, verify that its decay constant is -0.000121.

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

00:47

The half-life of carbon-14…

04:50

The half-life of a radioac…

01:07

A sample of carbon-14 has …

01:52

The radioactive isotope ca…

06:03

Radioactive Decay. Carbon-…

04:48

02:06

Involve exponential decay.…

01:04

What is the half-life for …

04:35

The half-life for the radi…

02:57

Use the radioactive decay …

Given that the half life of radioactive carbon 14 is 5,745 years. We are asked to verify that the decay constant is negative. 0.0001-1. So you can see that the form that we're going to be using is bubbled in in green right here. The half life we're told is that 5745 years equal to Ln two divided by. Okay. Which is that decay constants? Let's go ahead and just saw for the decay constant. To verify that it is that value that was given to us. So moving things around a little bit, we can see that K will be equal to The Natural Log of two divided by 5745. And this gives us a value of one point on the calculator, at least 1.2065 And scientific form times 10 to the negative fourth. So this does check out. If we were to bounce up decimal place back, we would get 0.000121 after rounding. And of course that would be negative because it is a decay constant. So this checks out. We can indeed verify that the decay constant is equal to the value that was given.

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