3 1. (02.01 H0) The total amount of rainfall, in centimeters, as a function of time, in days, is modeled by the function f, where g is a differentiable function. The data in the table gives values of g(t) at selected values of t, J? for 25rd! l I\")? gm for 89514 ' t 8 10 12 14 9(2) 2.25 2.05 1.75 1.45 Part A: what is the average rate of change of the amount of rainfall from day 8 to day 14, according to function f? (5 points) Part 3: Use the data in the table to approximate f'(9). Show your work. (5 p AP Calculus BC 0L v3 A -- Kivisto, Ruth - Activities Part o: Is fa continuous function from 2 5 ts 14? Explain. (10 points) Part D: Find f'(6) using the limit denition of the derivative. Show your work and explain its meaning. (10 points) j 2. (02.02 HC) When food is left out at room temperature for a long period of time, mold begins to grow on it. For 0 s t s 40, the amount of mold on an apple pie is modeled by the twicedifferentiable function A, where A(t) is measured in millimeters and t is measured in days. Values of A(t) at selected values of time t are shown in the table. r (days) 0 1 0 20 40 A(t)(m|lllmeters) 0.369 1.368 5.071 69.698 Part A: Use the data in the table to approximate A'(15). Show the computation that led to your answer. (10 points) Part B: Using correct units, interpret the meaning of A'(1 5) in the context of the problem. (10 points) Part c: The amount of mold is also modeled by the twice-differentiable function 8 for 0 5 ts 40, where B(t) is measured in millimeters and time t is measured in days. It is known that B(t) can be modeled by the function B(t) = 0.369(1.14)', where B(t) is measured in millimeters and t is measured in days. Using graphing technology, nd the value ofB'(15). (10 points) The graph of continuous function f for -3 s x s 16 is shown. 3 2 X -1 -2 -3 -4 -4 -2 2 4 6 8 10 12 14 16 18 20 Let g and h be functions defined by g(x) = In(x) . f(x) and h(x) = 4x2 + 3x - 2ex. Part A: Find g'(7). (10 points) Part B: The function m is defined by m(x) = f(x) . h(x). Find m'(0). (15 points) Part C: The function n is defined by n(x) = (2. Find n'(11). (15 points) f ( x )