complex formula for growth and decay help (1 Viewer)

[Halo189]

Q7 a piece of meat, initially at 14 degrees is placed in a freezer whose temperature is a constant -10 degrees. After 25 seconds the meat is 11 degrees.
Find
a) the meats temperature after 5 minutes
b) when the temperature will reach -8 degrees (to the nearest minute)

 

[photastic]

Assume Newton's Law of Cooling,
T = B + (A-B)e^-kt where T is in degrees, B and A are constants and t is in seconds.
Initially 14 means A=14
Constant temperature is -10 so B=-10

So T = -10 + 24e^-kt
when t=25, T=11, solve for k,
11 = -10 + 24e^-k(25)
e^-k(25) = 21/24
k=ln(7/8)/-25

a) When t=300 T = -10 + 24e^-(ln(7/8)/-25)(300) = -5.166 degrees

b) Simply solve for t when T=-8

 

[Halo189]

Assume Newton's Law of Cooling,
T = B + (A-B)e^-kt where T is in degrees, B and A are constants and t is in seconds.
Initially 14 means A=14
Constant temperature is -10 so B=-10

So T = -10 + 24e^-kt
when t=25, T=11, solve for k,
11 = -10 + 24e^-k(25)
e^-k(25) = 21/24
k=ln(7/8)/-25

a) When t=600 T = -10 + 24e^-(ln(7/8)/-25)(600) = -9 degrees

b) Simply solve for t when T=-8

Sorry but the answer said fir 7 a its -5.2 degrees

 

[photastic]

Sorry but the answer said fir 7 a its -5.2 degrees

I apologise, I thought 6 minutes was 600 seconds

Correction:
When t=300 T = -10 + 24e^-(ln(7/8)/-25)(300) = -5.166 degrees

 

[Halo189]

I apologise, I thought 6 minutes was 600 seconds

Correction:
When t=300 T = -10 + 24e^-(ln(7/8)/-25)(300) = -5.166 degrees

Thank you

 

[Halo189]

This is another question I'm not getting the answer too, I understanding the basics just don't know where I'm going wrong with this one

11. Whilhemy's law states that the rate of transformation of a substance in a chemical reaction is proportional to its concentration. That is dx/dt=k(x-c), where x is the amount of substance transformed and c is the initial concentration of the substance. Initially none of the substance is transformed. If the initial concentration is 7.9 and the amount transformed after 2 minutes is 2.7, find how much of the substance will be transformed after 5 minutes.

 

[leehuan]

Solve for k, find new expression, sub t=5

 

[Halo189]

Solve for k, find new expression, sub t=5

Thx