Chapter 6, Problem 25P

A mass balance for a pollutant in a well-mixed lake can be written as

$V\frac{dc}{dt}=W-Qc-kV\sqrt{c}$

Given the parameter values $V=1\times {10}^6{\text{m}}^3,Q=1\times {10}^5{\text{ m}}^3\text{/yr, }W=1\times {10}^6\text{g/yr,}$ and $k=0.25{\text{m}}^{0.5}{\text{/g}}^{0.5}\text{/yr}$, use the modified secant method to solve for the steady-state concentration. Employ an initial guess of $c=4{\text{g/m}}^3\delta =\mathrm{0.5.}$ Perform three iterations and determine the percent relative error after the third iteration.