Exercise #5: A hot liquid is cooling in a room whose temperature is constant. Its temperature can be modeled using the exponential function shown below. The temperature, T, is in degrees Fahrenheit and is a function of the number of minutes, m, it has been cooling. T(m)=10le -003m +67 %3D (a) What was the initial temperature of the water at m =0. Do without using your calculator. (b) How do you interpret the statement that T(60) = 83.7? (c) Using the natural logarithm, determine algebraically when the temperature of the liquid will reach 100 °F. Show the steps in your solution. Round to the nearest tenth of a minute. (d) On average, how many degrees are lost per minute over the interval 10 s m < 30? Round to the nearest tenth of a degree.

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