INTEGRATED MATHA common science experiment attempts to determine if mung bean seeds that are given a gentle zap in a microwave oven are more likely to sprout than mung bean seeds that are not given a zap. (a.) In such an experiment, what are the treatments (conditions you want to compare)? What is the response variable (outcome you are measuring)? (b.) For his experiment, Carlos zapped 10 mung bean seeds and 8 sprouted. Explain why Carlos should not conclude that mung bean seeds zapped in a microwave are more likely to sprout than if they had not been zapped. (c.) For her experiment, Mia took 20 mung bean seeds, picked out 10 that looked healthy and zapped them. Of the 10 that were zapped, 8 sprouted. Of the 10 that were not zapped, 3 sprouted. Explain why Mia should not conclude that mung bean seeds zapped in a microwave are more likely to sprout than if they had not been zapped. (d.) For her experiment, Julia took 4 mung bean seeds, selected 2 at random to be zapped, and zapped those 2. Both seeds that were zapped sprouted. The 2 seeds, that were not zapped not sprout. Explain why Julia should not conclude that mung bean seeds zapped in a microwave are more likely to sprout than if they had not been zapped. (e.) Design an experiment to determine if mung bean seeds, are more likely to sprout if they are zapped in a microwave. CALCULUSZamora Lopez, a candidate for the state senate, conducts weekly polls on her popularity from a pool of 50,000 voters selected at random. Suppose 5,000 people in the sample group favor Zamora's candidacy in the first poll (at time t = 0) and that in each successive poll, 1,200 new people per week favor her candidacy while 2% of the people who had previously favored her switch to her opponent. a. Set up an initial value problem for the number of people P(t) in the pool who favor Zamora after week t. b. Solve the initial value problem in part (a). c. The polling goes on for 21 weeks, with the final poll being conducted just before the election. If Zamora's polling model is accurate, should she expect to win or lose? d. Suppose that instead of increasing at the constant rate of 1,200 people per week, Zamora receives 125t new supporters per week at time t. Answer the questions in parts (a) through (c) for this revised polling model.