Question

The temperature at $12$ noon was ${10}^o$C above zero. If it decreases at the rate of $2^o$C per hour until midnight, at what time would the temperature be $8^o$C below zero? What would be the temperature at midpoint?

Answer 1

Given, $12$ noon temperature was ${10}^{o}C$ above zero.

$T\left(12pm\right)={10}^{o}C$

It decreases at the rate of $2^{o}C$ per hr until $12am$

$\frac{dT}{dt}$ (12pm to 12am) $=-2^{o}C$

$T\left(t\right)=-2t+T_0$

$T_0={10}^{o}C$

$-8^o=-2t+{10}^o$

$2t={18}^o$

$t=9$

It means at 9 pm, the temperature is $-8^{o}C$