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Zokunu

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20. A heated body is cooling. The excess of it's temperature above that of it's surroundings is Theta = Ae^-kt , where t is in minutes.

(a) If time t = 0, Theta = 80. Find A. Obviously...80.
(b) If the temperature of the surroundings is 20 degrees Celsius and the body cools to 70 degrees Celsius in 10 minutes, find:

(i) The body's temperature after 20 minutes.
(ii) The time taken to reach 60 degrees Celsius.



21. A radioactive substance decays at a rate that is proportional to the mass of radioactive substance present to any time. If 10% decays in 200 years, what percentage of the original radioactive mass will remain after 1000 years?

Step by Step if possible. THANK YOU SO MUCH.
 

photastic

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For 21 check the answers.
(Deleted the working out to hide the shame)

PS - Do you need to prove the M equation via integration? Some schools are required to do so.
 
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Zokunu

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B I) sub t=20 into theta?
Ah ferk, I got 61.25 degrees....when it is supposed to be 51.25 degrees.

Finding k so:

70=80e^-10k
k = 0.01335313926

Theta = 80e^-20k
= 61.25.

Little help?


Aarondapho soz that is completely wrong...57%.

ty
 

photastic

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OMG! In my previous attempt, I thought after 200 years, 10% is left. WHOOOPPPPPS
I got 59% because I stored the k value rather than rounding it off.
 

photastic

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Ah ferk, I got 61.25 degrees....when it is supposed to be 51.25 degrees.

Finding k so:

70=80e^-10k
k = 0.01335313926

Theta = 80e^-20k
= 61.25.

Little help?


Aarondapho soz that is completely wrong...57%.

ty
Question 20 is Newton's law of cooling. Your theta equation is wrong.



I might as well finish 20 b) (ii)
 
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