Problem 14c

Given information

As per the given question 

• The room temperature is  and and temperature of coffee is  

To find :

A rough sketch of the graph of the solution of the initial value problem (b)

Step-by-step explanation

Geometrically, when we impose an initial condition, we look at the family of solution curves and pick the one that passes through the point   

From part (b) the differential equation is,

And the initial condition is,

And referring to earlier part of  discussion,

The temperature is initially maximum and temperature decreases as   increases and approaches to the equilibrium that is the room temperature.

Therefore, if we try to draw the graph of  over  then graph is decreasing, up-to equilibrium.

Plot the - axis as vertical axis and - axis as horizontal axis and plot the graph as shown in figure