Question 1 According to the Michaelis-Menten equation, when an enzyme is combined with a substrate of concen- tration s (in millimolars), the reaction rate (in micromolars/min) is As R(S): K+s for positive constants A and K. (a) Show, by computing lim 12(3), that A is the limiting reaction rate as the substrate concentration _ 5}30 increases Without bound. (b) Show that the reaction rate attains one-half of the limiting value when the substrate concentration is K millimolars. Question 2 Ecologists predict the population of whitetailed deer in the state of Kentucky t years after 2004 will be 1, 072, 764e0'231 1' 0.19196 + 60-2311" According to the ecologists' model, what is the long term population of white-tailed deer? P(t) = Question 3 After an oil spill in thelGulf of Mexico, it is estimated that the concentration of oil in the water will total C(t) : 20 + 856'W mg per liter, where t is the number of years after the spill. (a) A safe concentration for the environment is considered to be 30 mg per liter. How long will it take before the concentration levels reach this amount? (b) What is the concentration of oil in the water expected to be in the long term? 00 uestion 4 Because the form is indeterminate, knowin that functions and satisf g 9 y 00 hm ax) = gm ya) = as mm tells us very little about . xmc 9(3) (a) Find formulas for f and 9 such that lim M is an 2 form that has a limit of 00. Hoe 9(2) 00 (b) Find formulas for f and 9 such that lim @ is an E form that has a limit of 0. H06 9(2) 00 (c) Find formulas for f and 9 such that lim M is an 2 form that has a limit of 1. Hoe 9(3) 00 ((1) Find formulas for f and 9 such that lim @ is an E form that has a limit of 13.72. Hoe 9(3) 00 Hint: you can answer each part by choosing f and g to be appropriate polynomials. Question 5 Because the form 0 - 00 is indeterminate, knowing that functions f and g satisfy lim f(:t:) : 0, lim 9(a) : oo 1)90 17}00 tells us very little about 1114191C f (r)g($). (a) Find formulas for f and 9 such that zh{Iolc f(az)g(:t) is a 0- 00 form that has a limit of 00. (b) Find formulas for f and 9 such that 2133:; f(a:)g(a:) is a 0- 00 form that has a limit of 0. (c) Find formulas for f and 9 such that Iling); f(:t)g(:i:) is a 0- 00 form that has a limit of 1. ((1) Find formulas for f and 9 such that all{Ea f(a:)g(a:) is a 0- 00 form that has a limit of 13.72. Hint: you can answer each part by choosing f (:3) and 9(a) to each be of the fawn Cm\" for appro- priate constants C and p. Question 6 Question 7 For f (I) : 233.922\