Question

Help me, Thanks!!

1）A room is being heated at the rate of r(t) = (0.3t)1/2, where r(t) is measured in degrees Fahrenheit per minute. If the temperature in the room at 6:00 AM is 50 degrees, what is the formula that will describe the temperature at 9:00 AM? Where T(t) = temperature at time t. Do not evaluate the integral.
2）The temperature in a room is being changed at rate of r(t) = -t2 + 3t, where r(t) is measured in degrees Fahrenheit per min. If the temperature in the room at 4:00 AM is 80 degrees, what formula will describe the temperature at 8:00 AM? Let T(t) describe the temperature at time t. Do not evaluate the integral.

Answer 1

2.) dT/dt = -t^2 + 3t

dT = (-t^2 + 3t)dt

T = -t^3/3 + 3t^2/2 + C

at 4:00 AM

80 = -4^3/3 + 3*4^2/2 + C

C = 80 + 4^3/3 - 3*4^2/2

C = 77.33

T = -t^3/3 + 3t^2/2 + 77.33

at 8:00 AM

T = -8^3/3 + 3*8^2/2 + 77.33

T = 2.67 deg