The growth in population of a certain colony of individuals is modeled by the eq

Question

The growth in population of a certain colony of individuals is modeled by the equation P_t=P_0e^(rt), where Pt is the population at time t, P_0 is the population at t = 0, and r is the yearly growth rate. Write a user-defined function that uses this model to predict the population at any time t, from knowing P0 and Pt1 at some other time t1. For function name and arguments use:

Pt = calculatePop(P0, Pt1, t1, t)

where the output argument Pt corresponds to Pt, and the input arguments P_0, P_t1, t1, t corresponds to P0, Pt1, t1, t, respectively.

Use the function for the following two cases:

(a) The initial population of a certain species is 50 million and it doubles in 20 years. Calculate the population 10 and 15 years from the initial time.

(b) The half-life of a radioactive material is 5.8 years. How much of a 7-gram sample will be left after 30 years.

The output should be displayed with meaningful messages.

Please answer in MATLAB! thank you.

Explanation / Answer

Function :

function Pt = calculatePop(P0, Pt1, t1, t)
r = log (Pt1 / P0) / t1;
Pt = P0 * exp(r*t);
end

==========================

Pt = calculatePop(50, 100, 20, 10);
X = sprintf('Population after 10 years = %.2f million',Pt);
disp(X);
Pt = calculatePop(50, 100, 20, 15);
X = sprintf('Population after 15 years = %.2f million',Pt);
disp(X);
Pt = calculatePop(7, 3.5, 5.8, 30);
X = sprintf('Sample left after 30 years = %.2f grams',Pt);
disp(X);

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output

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