TeamHw2 - Problem 2 : Let F ( x ) = Z 2 x x e-t 2 dt. 1....

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Math 116 Winter 2012 Team Homework 2 Problem 1 : The birth rate B ( t ), in cells per hour, of a bacteria population is given in the figure below. The curve marked D ( t ) gives the death rate, in cells per hour, of the same population. B(t) D(t) 0.5 1.0 1.5 2.0 2.5 3.0 t 0.2 0.4 0.6 0.8 1. At time t = 0, the population has size P 0 . Let P ( t ) be the size of the population at time t . Find a formula for P ( t ). 2. Estimate the time at which the population has a maximum. 3. Does the function P ( t ) have inflection points?
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Unformatted text preview: Problem 2 : Let F ( x ) = Z 2 x x e-t 2 dt. 1. Use your calculator to compute the values of F ( x ) for x =-2 ,-1 , , 1 , 2. 2. Is the function F ( x ) an odd function? Hint: Use the substitution u =-t to check if F (-x ) =-F ( x ). 3. For what values of x is F ( x ) increasing? 4. For what values of x is F ( x ) concave up? 5. Sketch the graph of F ( x ). Problem 3 : Section 7.1 # 98. Problem 4 : Section 7.1 # 112. 1...
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