 Hello and welcome to the session. In this session we will discuss a question which says that a cup of coffee is initially at a temperature of 93 degrees Fahrenheit, the difference between its temperature and the room temperature of 68 degrees Fahrenheit decreases by 9% each minute, write a function describing the temperature of coffee as a function of time. Now let us start with the solution of the given question. Now where we are given the initial temperature of coffee is 93 degrees Fahrenheit and the room temperature is 68 degrees Fahrenheit. It is given that the difference between the room temperature and the temperature of coffee is decreasing by 9% each minute. Now first we find initial difference between the temperature of coffee and room temperature. It will be 93 degrees Fahrenheit minus 68 degrees Fahrenheit which is equal to 25 degrees Fahrenheit. Thus difference in the two temperatures is 25 degrees Fahrenheit. Now this difference is decreasing by 9% each minute. So here we are given decreasing rate. Thus at time 10 minutes the difference in temperature will be given by 25 into 1 minus r the whole raised to power t here is decreasing or decreasing rate here r is equal to 9%. So difference in temperature is 25 into 1 minus 9% the whole raised to power t that is equal to 25 into 1 minus 9 upon 100 the whole raised to power t which is equal to 25 into 1 minus 0.09 when raised to power t which is equal to 25 into 0.91 raised to power t. Now let at any time t the temperature of coffee be capital T and the room temperature is always constant so it will always be 68 degrees Fahrenheit. Thus at any time t the difference in temperature will be capital T minus 68 now for the difference between temperatures that is capital T minus 68 we have already found the expression that is 25 into 0.91 the whole raised to power t. So we have the equation capital T minus 68 is equal to 25 into 0.91 raised to power t. Now adding 68 on both sides of this equation we get capital T minus 68 plus 68 is equal to 25 into 0.91 raised to power t plus 68. Now solving this implies capital T is equal to 25 into 0.91 raised to power t plus 68 where capital T is temperature of coffee at any time t. Thus this function describes the temperature of coffee as a function of time. Now where we have combined standard functions using alphanatic operation room temperature is always constant thus 68 is the constant function which is combined with the exponential function given by 25 into 0.91 raised to power t using addition. And here we have written a function describing the temperature of coffee as a function of time and this is the solution of the given question that's all for this session. Hope you all have enjoyed the session.