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# Exponential decay formula. Watch

1. I have designed a chart in excel, that shows concentrations of HCl (molL^-1) on the y axis and the effects on Marble over time (x axis). Basically the time for a solid marble chip to dissipate in HCl, chemical reaction.

Each Marble chip is 0.1 grams.

I need to somehow work out a decay rate for the following formula, i am not dealing with carbon-14, this is for CaCO3(s).

P(t) = P0e-rt
P(t) = the amount of some quantity at time t
P0 = initial amount at time t = 0
r = the decay rate
t = time (number of periods)

P(t) = P0.1 * e(- 3.3% * 29.54)
P(t) = 0.1 * e(-0.033 * 29.54) (Convert percentage to decimal form)
P(t) = 0.0335216059942
P(t) = 3.35216060 x 10-2 (Mass)

This is for the first result on the chart. Chip #1 @ 0.1 grams, in 0.5 (molL^1) HCl dissipates in 29.54 minutes.

I figured if i have 30 columns
1/30 = 0.0333333....
0.33333 x 100 = 3.3333% i would just use this as my r = the decay rate.

Guess not, now im not sure if this is an appropriate equation for my graph exponential line (curved line that is most useful when data values rise or fall at increasingly higher rates). Advice on how to find a decay rate percentage?

Thank you.
2. By dissipates I take it you mean the mass is reduced to zero.

The model will never give this.

Instead of looking at your situation I will give you another example.

If , initially P=50 and P(10)=25 then so obviously .

Then .

Solve to find r.

.
3. (Original post by g-wizz)
I have designed a chart in excel, that shows concentrations of HCl (molL^-1) on the y axis and the effects on Marble over time (x axis). Basically the time for a solid marble chip to dissipate in HCl, chemical reaction.

Each Marble chip is 0.1 grams.

I need to somehow work out a decay rate for the following formula, i am not dealing with carbon-14, this is for CaCO3(s).

P(t) = P0e-rt
P(t) = the amount of some quantity at time t
P0 = initial amount at time t = 0
r = the decay rate
t = time (number of periods)

P(t) = P0.1 * e(- 3.3% * 29.54)
P(t) = 0.1 * e(-0.033 * 29.54) (Convert percentage to decimal form)
P(t) = 0.0335216059942
P(t) = 3.35216060 x 10-2 (Mass)

This is for the first result on the chart. Chip #1 @ 0.1 grams, in 0.5 (molL^1) HCl dissipates in 29.54 minutes.

I figured if i have 30 columns
1/30 = 0.0333333....
0.33333 x 100 = 3.3333% i would just use this as my r = the decay rate.

Guess not, now im not sure if this is an appropriate equation for my graph exponential line (curved line that is most useful when data values rise or fall at increasingly higher rates). Advice on how to find a decay rate percentage?

Thank you.
I hope that it is P(t)=P0e^(-rt) because if e isnt to the power of -rt it isnt a decay formula.

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4. (Original post by BabyMaths)
By dissipates I take it you mean the mass is reduced to zero.

The model will never give this.

Instead of looking at your situation I will give you another example.

If , initially P=50 and P(10)=25 then so obviously .

Then .

Solve to find r.

.

Thank you kindly, appreciate your input .
5. (Original post by g-wizz)
...
Some thoughts/musings - in case they're of any use:

The rate of reaction is going to be proportional to the surface area exposed to the acid and some function of the concentration of the acid - call it f(c)

Assuming your chip is a sphere (for the sake of calculation),

Volume = k(radius)^3 for some constant which isn't really important so I'll leave it as k.

So, dV/dt = dV/dr x dr/dt.
= 3kr^2 dr/dt.

But equally the rate of change of volume is proportional to the surface area and some function of the concentration = lr^2f(c) (for some constant l, and concentration c)

so lr^2f(c)=3kr^2 dr/dt.

So dr/dt = constant times f(c)

Integrating we have.

r = constant times "time to dissolve" times f(c)

If all the chips are the same size we end up with

f(c) times "time to dissolve" = constant
6. (Original post by ghostwalker)
Some thoughts/musings - in case they're of any use:

The rate of reaction is going to be proportional to the surface area exposed to the acid and some function of the concentration of the acid - call it f(c)

Assuming your chip is a sphere (for the sake of calculation),

Volume = k(radius)^3 for some constant which isn't really important so I'll leave it as k.

So, dV/dt = dV/dr x dr/dt.
= 3kr^2 dr/dt.

But equally the rate of change of volume is proportional to the surface area and some function of the concentration = lr^2f(c) (for some constant l, and concentration c)

so lr^2f(c)=3kr^2 dr/dt.

So dr/dt = constant times f(c)

Integrating we have.

r = constant times "time to dissolve" times f(c)

If all the chips are the same size we end up with

f(c) times "time to dissolve" = constant
Another great approach, thanks for your input appreciate it

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