Question on Exponential growth and decay (1 Viewer)

[Jeffski]

Can be refered to Fitzpatrick 3U Pg 129

A body, initially at room tempreture is 20 degrees , is heated so that the tempreture would rise 5 degrees/min if no cooling took place. Cooling does occur in accordance with Newtons law of cooling and the max tempreture the body could attain is 120 degrees. How long it take to reach 100 degrees?

Given Newton's law of cooling is:

T = P + Ae^-kt

Could you guys help me out pls?

 

[Mountain.Dew]

Can be refered to Fitzpatrick 3U Pg 129

A body, initially at room tempreture is 20 degrees , is heated so that the tempreture would rise 5 degrees/min if no cooling took place. Cooling does occur in accordance with Newtons law of cooling and the max tempreture the body could attain is 120 degrees. How long it take to reach 100 degrees?

Given Newton's law of cooling is:

T = P + Ae^-kt

Could you guys help me out pls?

using the information given in the question:

A body, initially at room tempreture is 20 degrees

so, when t = 0, T = 20 ==> 20 = P + Ae^(0) ==> 20 = P + A....(1)

the max tempreture the body could attain is 120 degrees

so lim (t --> infinity) T = 20
lim (t --> infinity) P + Ae^-kt = 120
P + 0 = 120
P = 120 ==> sub into (1)

so 20 = 120 + A --> A = -100

so T = 120 - 100e^-kt

is heated so that the tempreture would rise 5 degrees/min if no cooling took place

i can only get up to here. dont know how to interpret this...

 

[Jeffski]

the answer is 32.2mins, which is close enought

thx guys