Radioactive Decay Graph in y=mx+c form

In summary, the conversation discusses an equation relating the radioactivity of lead in marine core sediments to the depth of the sediment. The equation is given as AL=A0exponential - λL/s, with various variables defined. The task is to convert this equation into y=mx+C form, which is achieved by taking the natural logarithm of both sides and simplifying. The final equation has a negative slope of gradient lambda/s and an intercept of lnAzero.
  • #1
Rockerjabroni
1
0

Homework Statement



This is an equation relating radioactivity of lead in marine core sediments in comparison with the depth of the sediment.

The equation is AL=A0exponential - λL/s

Where AL = activity at depth L (Bqkg-1)
Where A0 = activity at depth 0 cm (Bqkg-1)
λ = decay constant 0.031 yr-1
L= sediment depth (cm)
s= sediment accumulation rate (cmyr-1)

I need to make this into y=mx+C form


Homework Equations



As above.

The Attempt at a Solution



Well Ln both sides gives me

Ln AL = Ln (A0exponential - λL/s)

Ln AL = (Ln A0) + (Ln*exponential - λL/s) (which cancels)

Ln AL = (Ln A0) - λL/s

Ln AL = y
Ln (A0) = c
L= x
1/s = m

Is that correct? The graph has to be Ln AL against L but I wasn't sure about m and c. Thanks :)
 
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  • #2
Hello Rockerjabroni your equation is correct.If you now compare this to y=mx+c you should see that the graph has a negative slope of gradient lambda/s and intercept lnAzero.
 

1. What is a radioactive decay graph in y=mx+c form?

A radioactive decay graph in y=mx+c form is a graph that shows the relationship between the amount of a radioactive substance and the time it takes for that substance to decay. The graph follows a linear equation, y=mx+c, where y represents the amount of the substance, x represents time, m represents the rate of decay, and c represents the initial amount of the substance.

2. How do you plot a radioactive decay graph in y=mx+c form?

To plot a radioactive decay graph in y=mx+c form, you will need to determine the initial amount of the substance and the rate of decay. Once you have these values, you can plot the initial amount on the y-axis and the time on the x-axis. Then, use the slope (m) to determine the rate of decay and plot the points on the graph accordingly. Finally, use the y-intercept (c) to plot the initial amount of the substance on the graph.

3. What does the slope (m) represent in a radioactive decay graph in y=mx+c form?

The slope (m) in a radioactive decay graph in y=mx+c form represents the rate of decay of the substance. It indicates how much of the substance decays over a given period of time. The steeper the slope, the faster the rate of decay.

4. How can you use a radioactive decay graph in y=mx+c form to determine the half-life of a substance?

The half-life of a substance can be determined by finding the point on the graph where the y-value is half of the initial amount. This point will be the x-intercept, which represents the amount of time it takes for half of the substance to decay. You can also use the slope (m) to calculate the half-life by dividing the initial amount by two and then dividing that value by the slope.

5. Can a radioactive decay graph in y=mx+c form be used to predict future decay?

Yes, a radioactive decay graph in y=mx+c form can be used to predict future decay. By extending the graph beyond the plotted points, you can estimate the amount of the substance at a future time. However, it is important to note that this prediction is based on the assumption that the rate of decay remains constant over time.

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