a) A Suppose that a hot pocket is placed into an old and unreliable oven, which

Question

a) A Suppose that a hot pocket is placed into an old and unreliable oven, which is then turned on. The temperature of the hot pocket out of the freezer is 30 degree, and the oven temperature is gradually rising from t = 0 to t = 30 (in minutes), with the temperature at time t given by 70 + 10t. Suppose the heat constant of the hot pocket is .2. What is the temperature of the hot pocket at the end of 30 minutes? What if the oven had been pre-heated and was already at 370 degree when the hot pocket was put in?

Explanation / Answer

Let y b the hot pocket temprature i.e 30 min , that means

y(0)=30    at oven temprature 0 hotpocket temprature is 30

Change in temprature of Hot pocket= Heat constant( oven temperature at time t - Hot pocket temperature)

i.e.       y'=0.2(70+10t-y) and y(0)=30

y'= 14+ 2t-0.2y

we need to solve the initial value problem and get the general solution

put the general solution equal to 30 when t=0 and solve for C

then substitute t=30 to get the temprature

If the oven were preheated, we would get T(t) to be the constant function T = 370

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