Question

I need to figure out how to solve this with MATLAB if anyone could give me a hand.

Problem 3 The number of bacteria NB measured at different times t is given in the table in Figure 3. Determine an exponential function in the form NBNeat that best fits the data. Use the equation to estimate the number of bacteria after 4.5 hr. Make a plot of the points and the equation t (hr) N2,0004,500 7,500 15,000 31,000 64,000 Figure 3: Data Table Problem 3

Answer 1

Formulation:

Code:

t = 1:6;

NB = [2000 4500 7500 15000 31000 64000];

%estmating exponential function using linear regression

Y = log(NB);

%to get coefficients m and c

p = polyfit(t, Y, 1);

m = p(1);

c = p(2);

%plotting data

scatter(t, NB);

grid on;

hold on;

%calculating N with above equation

N = exp(c);

%calculating N with above equation

alpha = m;

%our determined exponential fit function

NBE = N.*exp(alpha.*t);

plot(t, NBE);

title("Number of bacteria vs Time");

xlabel("Time (in hours)");

ylabel("Number of bacteria NB");

legend("Data", "Exponential Fit");

%estimating number of bacteria at t = 4.5hr

Nq = N*exp(alpha*4.5);

fprintf("Number of bacteria at t = 4.5hr : %d",fix(Nq));

Output: