Deriving the Decay Rate Function from Mass & Time Graphs

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SUMMARY

The discussion focuses on deriving the decay rate function from mass and time graphs, specifically using the formula m = m(0) * e^(-kt). Participants emphasize the importance of plotting log(m) against time (t), which results in a straight line graph. Key parameters identified include a log(m) intercept of 4.5 and a gradient of -0.25, which directly relate to the decay rate. The conversation also touches on the relationship between mean line, half-life, and decay rate, suggesting that understanding these concepts is crucial for accurate analysis.

PREREQUISITES
  • Understanding of exponential decay functions
  • Familiarity with graphing techniques in data analysis
  • Knowledge of logarithmic transformations
  • Basic concepts of half-life in decay processes
NEXT STEPS
  • Research the derivation of the decay constant (k) from linear regression of log(m) vs. t
  • Learn about exponential fitting techniques for data analysis
  • Study the relationship between half-life and decay rate in radioactive decay
  • Explore the application of the formula m = m(0) * e^(-kt) in real-world scenarios
USEFUL FOR

This discussion is beneficial for students in physics or chemistry, researchers analyzing decay processes, and data analysts working with exponential models in various scientific fields.

sina_m7
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Hi.
We are given a table containing values of mass(m) and time(t). We have been asked to plot graphs of (m) against (t) and then log(m) against (t).

The question is:
FROM YOUR GRAPHS, DETERMINE THE FUNCTION FOR THE RATE OF DECAY.

Of course i know the formula but have no clue how to derive that. i need some help.
 
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when you say rate of decay are you referring to the half life? and you don't need to derive it but just say how your data supports it. Do you have any more specific information on your problem? such as your results for the m vs t and log(m) vs t?
 
dacruick said:
when you say rate of decay are you referring to the half life? and you don't need to derive it but just say how your data supports it. Do you have any more specific information on your problem? such as your results for the m vs t and log(m) vs t?

sorry, for the "rate of decay" I am referring to the formula m=m(0)*e^-kt

I have the following info when plotted log(m) vs t:
It is a straight line graph,
c(log(m) intercept) = 4.5
gradient = -0.25
 
so what would be your rate of decay from the graph?
 
Hi,
do you about the relations between meanline, halflife, decay rate and their invese..?
Just relate then and see you will get the answer.
You can also do a exponential fit for your plot!
good luck
 
thats what i need help with
 

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