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melbel
 2 years ago
Best ResponseYou've already chosen the best response.0I can't figure out how to solve these rate of decay questions, so I just made up my own as a way to help me learn this. How would I solve this?

Spectrum
 2 years ago
Best ResponseYou've already chosen the best response.0if it has a half life of 650 time units it means every 650 time units 1/2 of the samle dissapears.

melbel
 2 years ago
Best ResponseYou've already chosen the best response.0Yep. :) How would I find the rate of decay, though?

Spectrum
 2 years ago
Best ResponseYou've already chosen the best response.0halflife= ln2/k that is the half life equation

melbel
 2 years ago
Best ResponseYou've already chosen the best response.0I have a formula \[N=N _{0}e ^{kt}\] How/where would I plug everything in?

melbel
 2 years ago
Best ResponseYou've already chosen the best response.0I'm not sure I understand @Spectrum

prettyboy20202
 2 years ago
Best ResponseYou've already chosen the best response.0i gave him all right answers

prettyboy20202
 2 years ago
Best ResponseYou've already chosen the best response.0for his teset he did good to

ktnguyen1
 2 years ago
Best ResponseYou've already chosen the best response.0I think they are asking for k you got N=1/2No t=650 so you plug all numbers in and find k

melbel
 2 years ago
Best ResponseYou've already chosen the best response.0I mean, I don't understand what he meant. I'm having a lot of trouble with logarithms, so I'm not quick on my feet. :P

melbel
 2 years ago
Best ResponseYou've already chosen the best response.0\[N=\frac{ 1 }{ 2 }N _{0}^{650k}\] Okay, so what do I do next?

melbel
 2 years ago
Best ResponseYou've already chosen the best response.0Would I put some test number in for No? Like 100 or something?

ktnguyen1
 2 years ago
Best ResponseYou've already chosen the best response.0no,dw:1354966748637:dw you plug 1/2No for Nthen you can simplify for No

ktnguyen1
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1354967053153:dw

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1354952485674:dw

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1354952600983:dw

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1354952743876:dw

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1354953110349:dw

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0I think now it makes sense. Doesn't it?

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0KIS means keep it simple.

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1Derp still need help understanding =/

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1The easiest way I believe is to derive it from calculus (if you've taken Diff EQ , you should know how to). Doing this you get an equation much like yours only N_0 is denoted c \[A=ce^{kt}\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1now we're given two values to find what c is you need to know that \[N(0)=N_0\] \[N_0=ce^0=c\] \[N=N_0e^{kt}\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1same as your equation now we know that after 650 days , we will have half of the original amount soo \[N(650 days)=.5N_0\] \[.5N_0=N_0e^{650k}\] solve for k, divide by \[N_0\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{.5N_0}{N_0}=e^{650k}\] the initial N's cancel so you get \[.5=e^{650k}\] to get rid of e take the ln of both sides \[ln(.5)=650k\] \[\frac{ln(.5)}{650}=k\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1your rate of decay is \[\frac{ln(.5)}{650}=k\] your equation will be \[N=N_0e^{\frac{ln(.5)t}{650}}\]

ktnguyen1
 2 years ago
Best ResponseYou've already chosen the best response.0@Outkast3r09 : same thing I did. That is why I was confused with @mahmit2012 had done

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{dP}{dt}=kP\] \[\frac{dP}{dt}kP=0\] \[e^{\int{kdt}}=e^{kt+c}=ce^{kt}\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1you integrate the left side you'll just get that and the right side will be P
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