50 A train moves along a straight line. Its location at time t is given by 5(1) = T' 2 sts 7, where t is measured in hours and s(t) is measured in kilometers. Complete parts (a) - (c) below. (a) Graph s(t) for 2 s t s 7. Q A. O B. S 50 0' 50 4O 40 30 Q 30 20 20 1o 1 , 10 o E' o 0246810 0246810 dN Assume that N(t) denotes the size ofa population at time t, and that in some conditions N(t) satisfies the differential equation F = rN, where r is a constant. (a) Find the per capita growth rate. (b) Assume that rAB. If x(t) denotes the concentration of AB at time t, and k is the rate constant for the reaction, explain why E = (a x)(b - x), where k is a positive constan and a and b denote the concentrations ofA and B, respectively, at time 0. Also use the bracket notation [A], [B], and [AB] to denote the concentrations of chemicals A, B, and AB, respectively at tim t. (E d AB is produced at a rate 3MB] = V Producing one molecule of AB removes one molecule ofA and one molecule of B. Then [A]: V and [B] = V Since [AB] =x(t), make the dx substitutions to give = k(a x)(b x). dt Consider the function 9 given by g(x) = I x2 + 10'. Graph the function and. on the basis of the graph. guess where the function is not differentiable. Choose the best graph below. OA. OB. OD- Graph the piecewise-defined function. f(x) = 3x if X