Chapter 2.1, Problem 36P

Program Plan Intro

Program Description: Purpose of problem is to solve the equations $\frac{\left(5.308\right)M}{5.308+\left(M-5.308\right)e^{-50kM}}=23.192$ and $\frac{\left(5.308\right)M}{5.308+\left(M-5.308\right)e^{-100kM}}=76.212$ for the value of $k$ and $M$ .

Summary introduction: Solve the first equation for the quantity $x=e^{-50kM}$ and the second equation for $x^2=e^{-100kM}$ . Upon equating the two resulting expression for $x^2$ in terms of $M$ , the obtained equation is readily solved for $M$ and with known $M$ , substitute either of the original equations and readily solved for $k$ .