If a piece of metal is heated to temperature `theta` and the allowed to cool in a room which is at temperature `theta_0`, the graph between the temperature T of the metal and time t will be closet to

Options

A.
B.
C.
D.

Answer

C

Explanation

`(d theta)/(dt) =- k (theta-theta_(0)), underset(theta_(0))overset(theta)int(d theta)/(theta-theta_(0))=-Kintdt`
log `(theta -theta_(0)) =-Kt + C rArr theta - theta_(0) = e^(-Kt+C)`
`theta = theta_(0) +e^(Kt+C)` .