The temperature of a cake is given by the formula
T = 22 + 200e^-0.15t
Where T is the temperature of the cake (degrees Celsius) and t is the time in minutes after the cake is taken out of the oven.
At what rate is the temperature of the cake changing 20 minutes after the cake is taken from the oven?

Question

The temperature of a cake is given by the formula 
T = 22 + 200e^-0.15t
Where T is the temperature of the cake (degrees Celsius) and t is the time in minutes after the cake is taken out of the oven.
At what rate is the temperature of the cake changing 20 minutes after the cake is taken from the oven?

dumbcow · Answer

you need to find T'(20)

take derivative of T
hint
$$\large \frac{d}{dt} e^{f(t)} = f'(t)e^{f(t)}$$

anonymous · Answer

DT/dt = 200 (-0.15e^-0.15t)?

dumbcow · Answer

yep

anonymous · Answer

I inserted 20 and i got -1.5 degrees celsius per min

anonymous · Answer

as my answer

dumbcow · Answer

yep depending on how you round...i get -1.4936

anonymous · Answer

oh yeah. sensible to round to nearest number tho right?

dumbcow · Answer

depends on the instructions ... i would say default is to 2 decimals

anonymous · Answer

ah ok, thanks for the help

dumbcow · Answer

yw