Question

A tea of 45°C was emptied by Tunde. If the temperature at half cup level was 30°C after 2 minutes. How long did he take to empty the cup if the final temperature was 20°C. Take the temperature of the surrounding as 15°C.

Answer 1

$$T(x)=A+Be^{-\frac{x}{X}}, A=15$$

$$T(0)=45=A+B=15+B\to B=30$$

$$T(2)=15+30e^{-\frac{2}{X}}=30\to 30e^{-\frac{2}{X}}=15$$

$$X=2.8854\ min$$

Thus,

$$20=15+30e^{-\frac{x}{2.8854}}$$

$$x=5.17\ min$$