Question

A solid object is dropped into a pond with a temperature of 20 degrees Celsius. The function f(t) = Ce(-kt) + 20 represents the situation where t is time in minuetes, C is a constant and k = 0.0399. After 4 minutes the object has a temperature of 35 degrees Celsius. What was the initial temperature of the object

Answer 1

Given :

A solid object is dropped into a pond with a temperature of 20 degrees Celsius.

The function f(t) = Ce(-kt) + 20 represents the situation where t is time in minutes, C is a constant and k = 0.0399.

To Find :

The initial temperature of the object.

Solution :

Putting t = 4 in given equation, we get :

$35 = Ce^{(-0.0399)\times 4)}+20\\\\15 = Ce^{-0.16}\\\\C = 15\times e^{0.16}\\\\C = 17.60$

Putting value of C in given equation, we get :

$f(t) = 17.60e^{-0.0399t} + 20$

Now, for initial temperature is given at t=0 s .

$f(t) = 17.60e^{-0.0399\times 0} + 20\\\\f(t) = 37.60^o\ C$

Therefore, the initial temperature of the object is 37.60° C.

Hence, this is the required solution.