Slope of N - t graph of radioactive decay

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The discussion centers on interpreting the slope of the N versus t graph for radioactive decay, represented by the equation N = N_o e^{-\lambda t}. Participants clarify that while the slope can be easily identified in the log N versus t graph as -λ, the slope in the N versus t graph is not straightforward. The inquiry highlights a need for understanding the relationship between the decay constant and the graph's slope. The conversation also touches on the importance of derivatives in interpreting these graphs. Overall, the main focus is on clarifying the slope's meaning in different graph representations of radioactive decay.
songoku
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Homework Statement
Please see below
Relevant Equations
##N=N_o e^{-\lambda t}##
1713067012655.png


I am not really sure how to interpret the slope. The equation is:

$$N=N_o e^{-\lambda t}$$

If the graph is N against t, then what is the slope?

I can find the slope if the graph is log:
$$log N=log N_o -\lambda t$$

So if the graph is log N against t, then the slope is ##-\lambda##

But if the graph is N against t, I have no idea what the slope is.

Thanks
 
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Are you familiar with derivatives?
 
Orodruin said:
Are you familiar with derivatives?
Yes. I understand your hint.

Thank you very much Orodruin
 
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