Problem $7.(25$pt$)$

The concentration of pollutant bacteria $c$ in a lake decreases according to

where,

$c(t)=75e^{-1\mathrm{.}5t}+20e^{-0\mathrm{.}075t}$

$t=$ time

$7\mathrm{.}1.$ Newton$-$Raphson Method $(30$pt$)$

Determine the time required for the bacteria concentration $(c)$ to be reduced to $9$ using

the Newton$-$Raphson Method with an initial guess of $t=6$ and a stopping criterion of

$0\mathrm{.}5\%.$

$t_0=6$

${}_s=0\mathrm{.}5\%$

True root $(t_r)$ of the problem is given.

$t_r=10\mathrm{.}6467822$

Compute relative approximate percentage error $({}_{a,i})$ and true error $(E_{t,i})$ in each

iteration.

Complete the table below

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