The attention of pollutant bacteria c(t) in a lake decreases according to the aftercited countenance (ace is cfu/ml):

c = 75e−1.5t + 20e−0.075t

We’ll manifestation multitudinous arrangements to individualize the date required restraint the bacteria attention to be mean to a certain plane of 15 cf u/ml.

(a) (5 pts.) Write a Matlab arrangement to explain this gist using Newton’s arrangement with an ini- tial divine of t0 = 0 and pause touchstone of 0.5% near not-absolute mistake. At each recurrence, your arrangement should print (i) recurrence estimate, (ii) neard appreciate of t, and (iii) near not-absolute mistake. Print your arrangement and the output of your arrangement, and apprehend them in your solutions.

**Matlab script:**

**newtMethod.m**

function [ it, t, cc] = newtMethod( f1, f2, c0, toler)

%find the primitive aproximation

c(1) = c0 – (f1(c0)/f2(c0));

%find the not-absolute eroor

cc = abs(c(1)-c0);

%loop recurrence factor

k = 2;

%while not-absolute eroor senior than 0.5%

while (cc >= toler )

%find the direct assesment of date

c(k) = c(k-1) – (f1(c(k-1))/f2(c(k-1)));

%find the updated date

cc = abs(c(k)-c(k-1));

%if concetration is near than 15, break

if f1(c(k))<= 15

break

end

%increment the loop iterator

k = k+1;

end

it=k;

t=c(k-1);

end

**Function wheedle from console:**

c= @(t) 75*exp(-1.5.*t) + 20*exp(-.75.*t)-15;

c1=@(t) (-1.5*75)*exp(-1.5.*t) + (20*-0.75)*exp(-.75.*t);

[iteration, date, mistake]=newtMethod(c,c1,0,0.005)