Exponential Decay (1 Viewer)

[Lukybear]

A heated body is cooling and the excess of its temperature, x, above that of its surroudnings is x=Ae^(-kt) where t is time in minutes

a)At time t=0, x = 80 find A
b)If the temperature of the surroudnings is 20, and the body cools to 70 in 10min, find

i) Temperature after 20min
ii) Time taken to reach 60

I couldnt get this... and yet it seems so easy

Ive got A=80
and for bi) by using calculator ive got 31.25

my k was something like 0.04.... by calculator ofcoruse

Did anyone see my mistake or is the book wrong?

 

[Cazic]

The body cools to 70 in 10 mins (with a surrounding temp of 20), so:



Now, the temperature of the body after 20 minutes is the surrounding temp + excess temp, that is:



Finally, the body is 60 degrees when x(t) = 40, that is,



Or something like that.