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Cooling of a cup of tea

Let's have a delicious cup of tea

The initial temperature of the tea is 75°C and the room temperature is 24°C. Sketch the curve that you think it models the cooling temperature of the tea

Is it linear? is it quadratic? Justify

These are the temperatures at the beginning and after 3, 6 and 9 minutes have passed

Sketch the points in these set of axes

Can you see any tendency here? Explain briefly

This is the curve which models the cooling the temperature of the cup of tea

What is the y-intercept?

Does it have any roots? Why/Why not?

This is the equation of the curve

y = 24 + 51e-0.106x

What is the 'e' number?

Now that you know that the formula is that one, with 'e' approx to 2.72 and using the formula

Find the temperatures after 15, 20 and 40 minutes Remember: y = 24 + 51e-0.106x

What would you think it happens if the room temperature is another one?


Sketch the curve if the room temperature is now 15°C

What is the y-intercept?

15) Does the curve reach any minimum value? Which one? Why?

Are these two curves going to meet at any time? Why?/Why not?