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# As we saw in Section 3.8, a radioactive substance decays exponentially: The mass at time $t$ is $m(t) = m(0)e^{kt}$, where $m(0)$ is the initial mass and $k$ is a negative constant. The mean life $M$ of an atom in the substance is$$M = -k \int_0^\infty te^{kt}\ dt$$For the radioactive carbon isotope, $^{14} C$, used in radiocarbon dating, the value of $k$ is $-0.000121$. Find the mean life of a $^{14} C$ atom.

## 8264

#### Topics

Integration Techniques

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

The problem is, as we saw in section report eight. Right? You're active upstairs lace exponentially. My such Humpty is Teo To have zero taps need to the power create e Why are having zero is the initial mess on the K is a negative custom. I mean life. I'm at him. The substance? Yes, Um is the contradicted Kate house into girl from zero toe vanity? It has into the half, Katie, but the riders active coven. I said talk carbon fourteen used in Roy. Your carbon dating the value ofthe K iss negative zero points. There is a zero one one finds a mean life off carbon. Working at we have im is the contra native Kay. Lame it a cost in unity. It's a girl found zero toe pain. You need to create you. Yeah, first there were computers is afternoon tea into girl. If we light you, is we proud in tow? Then you promise he would want previously goto one. Okay. House needs power off Katie. Then we use integration. My part This is a two want over okay. Into past from zero to a minus. That limit minus the integral from zero to a one. Okay. It's okay. Yeah, this is Control one, over. Okay. House paid house. Need to. Okay. Minus one. Over. Okay. Quiet terms. You two. Okay, Eh? Minus why? But any goes to infinity? We have Lim. Okay? It's going to zero sense. Hey, is negative number and there's a limit. A handsome into K is also you come to zero, then we're half a mile. Is the connective Kay Holmes zero minus one. Broke a squire zero minus one. This is true. Negative one over. Okay, this is about painted too. Six, four point six three.

WZ

#### Topics

Integration Techniques

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp