Suppose that during the first few hours of a laboratory experiment, the temperature of a certain substance is closely approximated by the function f(t)-3-212+ St, where t is measured in hours, with 2-0 corresponding to the instant the experiment begins, and f(t) is the temperature (°F) of the substance after t hours. (a) Find an expression for Af/At using the interval [0, t). What are the units for Af/At? O p2/hr² OF2/min O °C/min O "F/hr O °C/hr (b) Use the result in part (a) to complete the following table. Round the answers to four decimal places. [0, 0.1) [0, 0.01] [0, 0.001] [0, 0.0001] Interval Af/At (c) In part (b), as the right-hand endpoint gets closer and closer to 0, what value does Af/At seem to be approaching? This target value tells us the rate at which the temperature is changing at the instant the experiment begins. F/hr

.Find the second derivative f"(x) for f(x) = e(æ+2)*.

For a given situation the initial value is 15 and the value of f( + 1) is always 49.2 times as large as the value of f(x).Which of the following expressions represents this situation? 49.2(0.85)" O 15(0.508)* О49.2(15)° 15(1.492)* O 49.2(1.15)" O 15(49.2)*

A tank contains 1000-gallon of pure water. Starting at time t = 0, a solution containing 0.2 lb of salt per gallon enters 10 gallons per minute and the well-stirred solution is withdrawn at a rate of 5 gallons per minute. Set up the initial value problem for the amount of salt, Q(t), in the tank as a function of t. Sove for Q(t).