exponential growth decay question help (1 Viewer)

[Mellonie]

Newtons LAw of colling stated that the rate of change of the temperature of an object is proportional to the difference between its temperature of the surounding matter. The temperature of the surrounding matter is assumed to be contant.

This may be expressed as dT/dt = K(T-P)

where P = constant temperatue surrounding medium
T= tempeature of the object which is a function of time t
K is a constant

The atmospheric temperature is assumed constant at 30'C. A metal object,heated to 125'C is placed in the ait to cool and after 1 hour is found to have cooled to 80'C. What will its temperature be after 1/1/2hours?

 

[FinalFantasy]

Newtons LAw of colling stated that the rate of change of the temperature of an object is proportional to the difference between its temperature of the surounding matter. The temperature of the surrounding matter is assumed to be contant.

This may be expressed as dT/dt = K(T-P)

where P = constant temperatue surrounding medium
T= tempeature of the object which is a function of time t
K is a constant

The atmospheric temperature is assumed constant at 30'C. A metal object,heated to 125'C is placed in the ait to cool and after 1 hour is found to have cooled to 80'C. What will its temperature be after 1/1/2hours?

consider an equation T=P+Ae^(kt) where A is a constant
DT\dt=kAe^(kt)=k(T-P)
.: T=P+Ae^(kt) is a possible equation.

T=30+Ae^(kt)
at t=0, T=125
125=30+Ae^0
A=125-30=95
at t=1, T=80
.: 80=30+95e^k
50=95e^k
50\95=e^k
ln (10\19)=k
at t=1\1\2 hrs,
T=30+95e^(3\2*ln(10\19))=.......