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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.

Help me, Thanks!! 1)A room is being heated at the rate of r(t) = (0.3t)1/2, where-example-1
Help me, Thanks!! 1)A room is being heated at the rate of r(t) = (0.3t)1/2, where-example-1
Help me, Thanks!! 1)A room is being heated at the rate of r(t) = (0.3t)1/2, where-example-2
Help me, Thanks!! 1)A room is being heated at the rate of r(t) = (0.3t)1/2, where-example-3
User Peit
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1 Answer

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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

User Jianru Shi
by
8.5k points

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