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Question 1:

5. (14 points) A calculator may be used. The rate of change of the population of moose, M(t), in the Boundary Waters Canoe Area Wilderness is directly proportional to 1200 M(t), for all t 2 0. 't' is the time in years and k is a constant of proportionality. When t= 0, the population is 300. b. Determine M(t) in terms of t and k. c. If M(4) = 600 find the value of k. J d. Calculate M(8) and explain its meaning in context of the situation. A continuously-decreasing function that is concave down on the interval [3, 7] is represented by the table. X 3 4.5 5 6.1 7 f(x) 1.946 1.705 1.609 1.361 1.099 Part A: Find the left Reimann sum estimate of ( f(x)dx, based on the subintervals given in the table. (4 points) Part B: Write the midpoint Reimann sum that estimates [, f(x)dx, based on the subintervals given in the table. (4 points)