Mathematics, 07.10.2020 22:01 dominiqueallen23

As a cake is pulled out of an oven, its temperature is greater than the temperature of the air in the kitchen, which is constant at 80 °F. The rate at which the temperature of the cake decreases at any time t is proportional to the difference between its temperature T(t) and the temperature of the air in the kitchen. A.23.a. Write the differential equation for the temperature T(t) of the cake at time t. A.23.b. Find the general solution to the differential equation. Show your work. Verify that your solution is correct by substitution. A.23.c. For your general solution in part A.23.b, and assuming that the temperature of the cake when initially removed from the oven is 350 °F, and that T(2 min) = 200 °F, determine T(2.5 min). Assume 2.7 as the approximate value of e (the exponential function), and use the logarithm chart in A.14 rather than a calculator. A.23.d. Plot the function T(t) vs. t for 0 ≤ t ≤ 20 min, assuming the initial condition provided in A.23.c. For instructions on what if means to plot the function, see instructions for A.15 - A.22. A.23.e. How many minutes after being removed from the oven does the cake reach 85 °F? Use the logarithm chart in A.14 rather than a calculator.

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As a cake is pulled out of an oven, its temperature is greater than the temperature of the air in th...

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