Tuesday, February 8, 2000

How do you calculate Leaf Decomposition?

I had to do a lab where we left leaves outside for 70 days to note their decomposition. My questions in my lab are: Calculate the daily decomposition rate (leaf tissue loss per day) for each litter bag. and. Calculate decomposition rate constant (k) for each litter bag...

the starting weights for both bag 1 and 2 were 3 grams. The final weigh for bag 1 was 2.57 g and for bag 2 was 2.36 grams.

If you could please help me calculate these it would be extremely helpful!
THANK YOU!

Answer on How do you calculate Leaf Decomposition?

It would really help to know if this is a high-school or college lab project and, if you have had any calculus before. When a problem ask for a "rate" of change, that suggest the use of derivatives.

Ok, you have to setup the initial condition and use the exponential decay equation. It will be in the form of Y = e(-x) or Y = Yo e(-kt)

You will need to solve the above equation (Y = Yo e(-kt)) for t = 0 ; where t = 0 is the starting point of your experiment.

The starting values was 3 grams per bag; thus,
3 = 3 e(-k(1)) the 1 represents day 1

3 = 3 e(-k)
solve for -k use natural logs for this purpose.

nl(3) = nl(3) + (-k) ln(e)

note: ln(e) cancels out and = 1

ln(3) = nl(3) -k(1)
ln(3) = nl(3) -k

-k = ln(3) - ln(3)
-k = ln (3/3)
-k = ln(1)
-k = 0 The constant -k of proportionality is zero at time, t = 0, at the start of the experiment.
-----------------------------
Now, we need the proportionality constant value at the end of your experiment. Take the results you got for bag #1 = 2.57 grams

Plug that into the decay equation for Y, and solve for the -k:

2.57 = 3 e(-k(70))
ln(2.57) = ln(3) -K70 ln(e)
ln(e) = 1
ln(2.57) = ln(3) -k70
-k70 = ln(2.57) - ln(3)
-k70 = ln(2.57/3)
-k70 = ln(0.857)
-k70 = -0.154
-k = -0.154 / 70
-k = -2.205 x 10^-3
-k = -0.002205 is your answer for bag#1 at the end of your lab project on day 70
----------------------
You can plug this value of -k back into your original decay equation (Y = Yo e(-kt)) or Y = 3 e(-k70) and it should give you 2.57 grams.
------------------------
I will leave it to your to work out the value of -k for bag #2
------------------------
Daily decompostion rate: Here's what I think you need for this part of the problem:

Y = Yo e(-kt)
dy/dt = (Yo e(-kt) (-k)

[dy/dt = -k Yo e(-kt)] is the equation you will want to use. Plug -k = -0.002205 into this equation, and then plug whatever day in the experiment (1 to 70) you want to know the decay value for.

I hope that's what you're looking for.

See: Exponential growth/decay
http://www.regentsprep.org/Regents/math/…

Good luck