Why Is an Exponential Model Suitable for Simulating Radioactive Decay?

[luysion]

~Radioactive decay simulation

Homework Statement

i have modeled a simulation of radioactive decay and am using an exponential model of y = Ae^kx

and I am asking to analyse my model and justify my choice of model.
and points I can discuss are relating the solution to the problem and explaining how the theory of the situation relates to your selected model

how would i do this?

Homework Equations

y - Ae^-kx

The Attempt at a Solution

using basic radioactive knowledge i guess the exponential model will give me an answer no matter what the time period e.g. it will give me an answer for a time period of a 100000 which is unrealistic as the atom should have completely decayed

 

[rl.bhat]

Define y, A, k and x.

 

[Bacat]

If you use the model $$y=Ae^{kx}$$, you will be probably be increasing, rather than decreasing, your population. This is why rl.bhat suggested defining your variables. Is y the population at time x? Is it the change in population? You need to know which direction this is moving.

Start with time zero and make sure you get 100% of the population. Then verify that the model decreases the population as time increases. When time goes to infinity, your population should go to zero.

If you have the ability to graph, try graphing the function and see how it changes. This can give you a big clue as to whether it is the correct type of function (increasing? decreasing? zero in the right place? 100% population in the right place) or not.

 

[luysion]

hey guys thanks for the reply. i found y = Ae^kx to be the most appropriate graph through use of linearisation (i.e. plotting ln y and x and getting semi straight line)

this was my equation y = 45e^-0.43t
the choices of models to choose from were the power function and the exponential function so i guess i really have to justify why exponential suits the THEORY behind radioactivity better than power function. and i also have to relate the solution to the problem.

 

[Bacat]

Do you know how to do a fit? If you can show that the exponential function fits the data points betters than the power function then you will have statistical evidence that it is the best model.

 

[luysion]

hey bacat,
yea i have done a fit also with R^2 showing that the exponential function is more appropriate,
but i need to explain how the theory of radioactive decay relates to my selected model.

i brain stormed this is this correct?; exponential graphs always have the same %change in y for the same increase in x, this would make it more appropriate for radioactive decay as it has a half life.?

 

[Bacat]

It's not a completely clear sentence the way you've written it now. Try using an outline like this:

1) A description of radioactive decay. A definition of half-life.

2) An explanation of exponential functions and how they describe the above description.

3) The specific function you chose.

4) The fit of your function to the data. A comparison with a power-series fit showing that the exponential has a lower r^2 value.

5) A conclusion stating that the exponential describes the important aspects of radioactive decay most accurately.

Write a sentence or two about each point and then arrange them into a paragraph.