Simple ratio?

[Essay]

This is from an online [EdX] introductory class in "climate science" ...of course:

 

 

Consider a simple model for the evolution of the concentation of a certain gas in the atmosphere,

dC/dt =

E – C/τ

 

where C is the concentration of the gas [Teragrams], E is the emission rate [Tg/yr], and t is time [yr]. The time-scale τ [tau in yr] represents the lifetime of the gas in the atmosphere, before it is removed, either by chemical reactions or deposition to the surface.

 

CFC-11, has an atmospheric lifetime of approximately 55 years. Suppose that all emission of CFC-11 ceased on January 1, 1988, a few months after the signing of the Montreal Protocol. Using the simple equation given above, find what year the concentration of CFC-11 would be reduced to one-fifth of its concentration at the beginning of 1988.

 

 

So tau = 55, and E = 0, from the information given, I assume. Seems to me, that if dC/dt is the ratio, and the concentration falls by 4/5ths,

then the decay time (t) [...the "solution"] would equal or 'fall by' that same 4/5 ratio ... when applied to tau.

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...and then adjusted for the baseline year, to find the answer to their question, right?

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It seems straightforward enough, and my 'solution' seems "realistic;" but my online 'answer' gets a red X, instead of the green checkmark.

What am I missing in the math, or misreading about the question, above here?

 

Thanks!

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[imatfaal]

what numerical answer do you get? Seems a fairly simple sum to me - but it would help to help you if we knew what you thought the answers was.

Have you checked with the forums that there isn't a marking error on that question - I spent over an hour on the charge distribution on a hollow sphere before reading that the forum software was marking incorrectly

 

 

And btw - the honour code on my edx courses said that I should not seek answers to any marked assignments etc. So any explicit answers to these questions may be hidden

[Essay]

what numerical answer do you get? Seems a fairly simple sum to me - but it would help to help you if we knew what you thought the answers was.

Have you checked with the forums that there isn't a marking error on that question - I spent over an hour on the charge distribution on a hollow sphere before reading that the forum software was marking incorrectly

 

 

And btw - the honour code on my edx courses said that I should not seek answers to any marked assignments etc. So any explicit answers to these questions may be hidden

Thanks, it may be a problem with the new course and software.

 

I got "44 years" as the dt [the 'solution' to the formula] ...when only 1/5 of the gas would be (is) remaining (from the way they worded the question).

 

I added that to 1988, to get "2032," which is the 'answer' they marked wrong.

 

I have considered trying 2031, thinking they could mean 1987 as the last full “baseline” year, but wanted to check my reasoning and math comprehension first. I'm not misunderstanding the whole dC/dt thing, I hope; this is just a simple linear relationship?

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If 44 sounds correct, I can still use that number to finish the other "parts" to the problem.

 

Thanks again!

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