Consider a biochemical ligand l that binds and unbinds a cell surface receptor raccording to the following: r+ lc where is the complex formed by r-c binding, k, and k are forward and reverse reaction rates assuming that the ligand concentration is constant (l.) and the total concentration of receptors is constant (tot) yields the following mass-action ode: at = kg (rtot - clo-k c a. find the exact solution for c(t) in this ode (hint: the equation is separable, and you can assume co - 0) b. suppose we are interested in a cell adhesion receptor that binds fibronectin substrates (rto 5x10 receptors per cell, lo = 1x10? m, k, = 7x10 /m-min, and k, = 0.6 /min). write a matlab code that uses (1) the forward euler's method, and (2) the classical runge-kutta (rk) method to approximate this ode solution from t = 0 to 3 minutes. for each method, try a couple different values for time-step size. plot the 4 numerical approximations (2 methods x 2 different step sizes) against the exact solution you found in part (a). also plot the cumulative global errors of each approximation vs. time-steps. c. for 6350 students calculate the "compute time" i. e., how long did the software take to perform the calculation) for each of the 4 approximations, and plot the 4 compute times vs. the 4 total global errors. (hint: matlab functions 'tic' and 'toc' should be .)