Hydrographs are used by civil engineers to model rainfall$-$runoff processes. A simple

analytical model for describing a stream hydrograph after a rainfall event $($i$.$e$.,$ increase in

stream flow as a function of time$)$ can be described by the equation:

$Q(t)=a*(\frac{t}{b}{)}^n*exp(n-(\frac{n*t}{b}))$

where a and $b$ are known constants $($model parameters$),t$ is time in hours and $Q$ is the

estimated flow in $f\frac{t^3}{h}r.$

Use Excel to implement the above equation and plot $Q(t)$ for $t$ ranging from $0$ to $20$ hours

with a step of $0\mathrm{.}5$ hrs $.$ Adopting $n=1\mathrm{.}2$ and $b=3\mathrm{.}1,$ generate flow data and professionally

plot four hydrographs with: $a=200,000$;$a=300,000$;$a=500,000,$ and $a=600,000.$ What

happens when we vary the constant $a?$

Repeat the process from Problem $4,$ adopting $n=1,a=300,000,$ and $b=1,2,4,6.$ What

happens when we vary the constant $b?$ You can make a copy from the previous tab and make

any necessary adjustments to quickly answer this problem.