Hello! I'm stuck on what to derive with the given information. Please and thank you!
Q: According to Newton's Law of Cooling, the temperature, T degrees Celsius, of a heated objected placed in a room with air temperature 20 degrees Celsius is modelled by the equation
T=20 + B e^(-kt),
where t is the time in hours the object takes to cool, and B is a constant. A cup of coffee has an initial temperature of 90 degrees Celsius. It cools down to 30 degrees in 20 min when the room temperature is 20 degrees. How long did it take for the cup of coffee to cool to 50 degrees?
What I know:
By finding the derivative of T, will give the maximized rate
T' = 0 + Be^(-kt) * (-k)
answer: 8.7 min approx
Thank you!
Q: According to Newton's Law of Cooling, the temperature, T degrees Celsius, of a heated objected placed in a room with air temperature 20 degrees Celsius is modelled by the equation
T=20 + B e^(-kt),
where t is the time in hours the object takes to cool, and B is a constant. A cup of coffee has an initial temperature of 90 degrees Celsius. It cools down to 30 degrees in 20 min when the room temperature is 20 degrees. How long did it take for the cup of coffee to cool to 50 degrees?
What I know:
By finding the derivative of T, will give the maximized rate
T' = 0 + Be^(-kt) * (-k)
answer: 8.7 min approx
Thank you!