When food is left out at room temperature for a long period of time, mold begins to grow on it. For 0 ≤ t ≤ 40, the amount of mold on a cherry pie is modeled by the twice-differentiable function C, where C(t) is measured in millimeters and t is measured in days. Values of C(t) at selected values of time t are shown in the table.

Part A: Use the data in the table to approximate C′(15). Show the computation that led to your answer.

Part B: Using correct units, interpret the meaning of C′(15) in the context of the problem.

Part C: The amount of mold is also modeled by the twice-differentiable function D for 0 ≤ t ≤ 40, where D(t) is measured in millimeters and time t is measured in days. It is known that D(t) can be modeled by the function D(t) = 0.357(1.14)t, where D(t) is measured in millimeters and t is measured in days. Using graphing technology, find the value of D′(15).