Deriving the Decay Rate Function from Mass & Time Graphs

In summary, the conversation revolved around plotting graphs of mass against time and log(mass) against time to determine the function for the rate of decay. The formula m=m(0)*e^-kt was mentioned, but the speaker needed assistance in deriving it and understanding how the data supports it. They also discussed the possibility of using an exponential fit and the relation between meanline, half-life, and decay rate. Ultimately, the focus was on finding the rate of decay from the plotted data.
  • #1
sina_m7
3
0
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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  • #2
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?
 
  • #3
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
 
  • #4
so what would be your rate of decay from the graph?
 
  • #5
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
 
  • #6
thats what i need help with
 

Related to Deriving the Decay Rate Function from Mass & Time Graphs

1. What is the purpose of deriving the decay rate function from mass and time graphs?

The purpose of deriving the decay rate function from mass and time graphs is to determine the rate at which a substance is decaying over a specific period of time. This information can be used to make predictions about future decay rates and to understand the behavior of the substance.

2. How do you calculate the decay rate function from a mass and time graph?

The decay rate function can be calculated by finding the slope of the tangent line at any point on the mass and time graph. This slope represents the rate of change of the mass over a small time interval, which is the decay rate at that specific time.

3. Can the decay rate function be negative?

No, the decay rate function cannot be negative. The decay rate represents the rate at which a substance is decreasing, so it will always be a positive value.

4. What are the units of the decay rate function?

The units of the decay rate function are typically given as mass per unit time, such as grams per second or kilograms per year. The specific units will depend on the units used for the mass and time axes on the graph.

5. How is the decay rate function related to the half-life of a substance?

The decay rate function is directly related to the half-life of a substance. The half-life is the amount of time it takes for the mass of a substance to decrease by half. The decay rate function can be used to calculate the half-life by setting it equal to half of the initial mass and solving for time.

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