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Question 9 [1 point} Find the derivative of each of the following functions. _ 4 _ 2 L _ 1. y 5a: 3H: + 7 2. f (m) : 5645\" eiJ1(m) 3'9 (33) : 321 \fAt time t {in clays}, the size S of a population of butterflies is given by the formula 600 1+ 49(013)t ' Use the graph above and your knowledge of derivatives to answer the following: 1. What is the growth rate after 10 days? 2. When does the maximum growth rate occur? 3. Explain why the shape of the graph looks this way. Question 11 [1 point] Carbon-14 is a radioactive substance produced in the Earth's atmosphere and then absorbed by plants and animals on the surface of the earth. It has a half-life (the time it takes for half the amount of a sample to decay) of approximately 5730 years. Using this known piece of information, scientists can date objects such as the Dead Sea Scrolls. The function N = Noe')\"E represents the exponential decay of a radioactive substance. N is the amount remaining after time t in years, No is the initial amount of the substance and A is the decay constant. 1. Find the rate of change of an initial amount of 1 gm of carbon-14 found in the scrolls, if the decay constant is given as A = 1.21 x 10-4. 2. If the percentage of carbon-14 atoms remaining in a sample is 79%, how old is the sample? Question 12 (1 point] A team of students seeks to make a flag representing their commitment to the ea rth. They will be using a green triangle inscribed in a yellow semi-circle. Find the maximum area of the triangle inscribed in a semi-circle of radius r