Newtons Law of Cooling - Determine rate of cooling

[Nokesy459]

An engine switched off and left to cool naturally will obey Newtons law of cooling.
A particular engine is switched off at 105°C when the ambient temperature is 0°C. Its temperature falls according to the equation T=105e-0.025t °C. Where t=time in minutes.

c) use calculus to determine the rate of fall of temperature when t=80 minutes



I have no clue where to start! no matter how hard i look there's nothing to help..

 

[BruceW]

The question asks for "the rate of fall of temperature" What does this mean in calculus?

 

[Nokesy459]

How do you mean?

 

[LawrenceC]

Have you had a course in calculus?

 

[Nokesy459]

No, This is self research and teaching

 

[LawrenceC]

I suspected that and was curious. I don't want to hijack BruceW's assistance...

 

[BruceW]

I don't mind others helping as well. The question asks for "rate of fall of temperature" Have you done similar problems, where you found the rate of change of some function?

 

[Nokesy459]

I have attempted, but the example i was using wasn't much help..

 

[LawrenceC]

Here's a simple example. Suppose temperature function is

T(t) = 2*e^(3t)

where t is time and T(t) is the temperature function in time.

The rate of temperature change is therefore

dT/dt = 6*e^(3t)

Can you take derivatives like the above?

 

[BruceW]

Lawrence has given a good example. There are a couple of simple rules for differentiating exponential functions. I'm guessing you've already done problems where you differentiated a polynomial function? Those are the kinds of functions that are learned first.

You need to learn about differentiation to do these kinds of problems. In some cases, there are simple rules for how to differentiate a function. And there are also things like the product rule and chain rule that can help us to differentiate more complicated functions. These are essential if you want to be able to master these kinds of problems!