problem 2 (total 50-points). Use the starter sheet provided to organize your answers. Bacteria grow rapidly in nutrient solutions. The growth rate dX/dt, where X is bacteria concentration [g/L] and t is time [hour or h ], is described by the following equation: dtdX=vX v is the specific growth rate [1/hour or h1]. A bacterium is grown to produce a bioproduct. At t=0, the process starts with addition of a seed culture, with X=0.1g/L. ( X0 is X at t=0.) In the nutrient solution used, v=0.9h1 for this bacterium. A. With a time step of t=0.25h, integrate the above ODE numerically to find the bacteria concentration X from t=0 to t=5h, using a. (I7-points) Euler's method b. (25-points) 4th-order Runge-Kutta method B. (4-points) Calculate X from t=0 to t=5h using the analytical solution of the above simple ODE: X=X0e(vt). C. (4-points) What would you change to improve the accuracy of the Euler's method solution for this calculation? Don't actually redo the solution. problem 2 (total 50-points). Use the starter sheet provided to organize your answers. Bacteria grow rapidly in nutrient solutions. The growth rate dX/dt, where X is bacteria concentration [g/L] and t is time [hour or h ], is described by the following equation: dtdX=vX v is the specific growth rate [1/hour or h1]. A bacterium is grown to produce a bioproduct. At t=0, the process starts with addition of a seed culture, with X=0.1g/L. ( X0 is X at t=0.) In the nutrient solution used, v=0.9h1 for this bacterium. A. With a time step of t=0.25h, integrate the above ODE numerically to find the bacteria concentration X from t=0 to t=5h, using a. (I7-points) Euler's method b. (25-points) 4th-order Runge-Kutta method B. (4-points) Calculate X from t=0 to t=5h using the analytical solution of the above simple ODE: X=X0e(vt). C. (4-points) What would you change to improve the accuracy of the Euler's method solution for this calculation? Don't actually redo the solution