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 May 27th, 2019, 04:31 PM #1 Senior Member   Joined: Mar 2019 From: TTF area Posts: 136 Thanks: 1 Graph half-life A radioisotope of Krypton has a half-life of 3.0s. A sample of krypton contains 1024x1024 undecayed atoms. Calculate how many undecayed atoms will remain after half a minute My solution → Firstly, I will change 3.0s to a minute 0.05 Then I figure out how many half-lives have been 0.5 (half a minute) / (divided by) 0.05=10 Then I, (1/2)^10=1/1024 change into a decimal 0.0009765625 Then lastly I will time (1024x1024) by (0.0009765625) to get 1x1024 undecayed atoms after half a minute. So I think it would be beneficial to also display this in a graph to show the decrease (decay) in half a minute. Can somebody do this for me, or show me how to? Last edited by greg1313; May 28th, 2019 at 12:52 AM. May 27th, 2019, 05:27 PM #2 Member   Joined: Oct 2018 From: USA Posts: 90 Thanks: 61 Math Focus: Algebraic Geometry Basic exponential form is: $f(t) = f_{0}e^{kt}$ $t$ is time in seconds, $f_{0}$ is the starting value, and $k$ is a coefficient we'll need to find. $f_{0} = 1024^{2}$ $f(3) = \frac{f_{0}}{2} = \left(\frac{1024^{2}}{2} \right)$ Now we solve for $k$ $\left(\frac{1024^{2}}{2} \right) = 1024^{2}e^{3k}$ $k = \left( \frac{ \ln(0.5) }{3} \right)$ So just graphing the equation $\displaystyle f(t) =1024^{2}e^{ \left( \frac{ \ln(0.5)t }{3} \right) }$ Should do the trick, here it is in Desmos: https://www.desmos.com/calculator/hj91obhfur May 27th, 2019, 05:41 PM #3 Senior Member   Joined: Mar 2019 From: TTF area Posts: 136 Thanks: 1 On demos have you put the number of undecayed atoms on the Y axis and the time on the X axis? May 27th, 2019, 05:46 PM #4 Member   Joined: Oct 2018 From: USA Posts: 90 Thanks: 61 Math Focus: Algebraic Geometry Yes May 27th, 2019, 06:03 PM   #5
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Quote:
 Originally Posted by helpmeddddd A radioisotope of Krypton has a half-life of 3.0s. A sample of krypton contains 1024x10^24 undecayed atoms. Calculate how many undecayed atoms will remain after half a minute My solution → Firstly, I will change 3.0s to a minute 0.05 Then I figure out how many half-lives have been 0.5 (half a minute) / (divided by) 0.05=10 Then I, (1/2)^10=1/1024 change into a decimal 0.0009765625 Then lastly I will time (1024x10^24) by (0.0009765625) to get 1x10^24 undecayed atoms after half a minute. So I think it would be beneficial to also display this in a graph to show the decrease (decay) in half a minute. Can somebody do this for me, or show me how to?
I forgot to place some ^ to the power of signs does this affect your graph?

Last edited by helpmeddddd; May 27th, 2019 at 06:05 PM. May 27th, 2019, 06:18 PM #6 Member   Joined: Oct 2018 From: USA Posts: 90 Thanks: 61 Math Focus: Algebraic Geometry Just change $f_{0}$ to $1024 \times 10^{24}$, so $\displaystyle f(t) =\left(1024 \times 10^{24} \right) e^{ \left( \frac{ \ln(0.5)t }{3} \right) }$ Thanks from helpmeddddd May 28th, 2019, 05:10 AM   #7
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Quote:
 Originally Posted by helpmeddddd . . . (1/2)^10=1/1024 change . . .
It can be left as 1/1024. The answer is therefore 10^24.

Producing a graph isn't necessary, but why not opt for a log graph, which would be a straight line? May 28th, 2019, 12:38 PM #8 Senior Member   Joined: Mar 2019 From: TTF area Posts: 136 Thanks: 1 Show me this log graph? May 28th, 2019, 03:59 PM #9 Global Moderator   Joined: Dec 2006 Posts: 20,969 Thanks: 2219 Why? It's just a straight line segment (starting at (0, 27) approximately) with a gentle negative apparent slope. The apparent slope depends on the scaling used, but if you plot the base 10 logarithm of the function Greens gave, the gradient is about -0.1. Tags graph, grpah, halflife Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post allylee Algebra 1 March 8th, 2013 05:26 AM Lucida Algebra 1 March 27th, 2012 02:35 PM usyer Physics 3 June 4th, 2011 05:47 PM jerakahol Algebra 10 January 10th, 2011 03:27 PM symmetry Algebra 3 July 7th, 2007 09:59 AM

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