Answer :
The Fibonacci model is a mathematical sequence that represents the growth of a population of rabbits. In this model, we start with no rabbits in month 0. At the end of month 1, a pair of infant rabbits is obtained, with one male and one female.
It's important to note that rabbit pairs are not fertile during their first month of life. However, starting from month 2, each adult pair of rabbits gives birth to one pair of rabbits (again one male and one female).
In this model, no rabbits die, so the population only grows. Let's go through some examples to understand how the model works:
- In month 0, there are 0 pairs of rabbits.
- In month 1, there is 1 pair of infant rabbits.
- In month 2, the infant pair has become adult rabbits, but there is still only 1 pair.
- In month 3, there is the 1 pair of adult rabbits and the one pair of infant rabbits produced by the adult pair. So, there are 2 pairs in total.
- In month 4, the adult pair will produce another infant pair, and the existing infants will become adults. This gives us 3 pairs in total.
The pattern continues, and we can see that the number of pairs of rabbits follows the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.
To write a MATLAB function that calculates the number of pairs of rabbits in month n, we can use the Fibonacci sequence. The function should accept an integer n ≥ 0 as input. Here's an example of how the function can be implemented:
```MATLAB
function [totalPairs, adultPairs, infantPairs] = fibonacciRabbits(n)
if n == 0
totalPairs = 0;
adultPairs = 0;
infantPairs = 0;
elseif n == 1
totalPairs = 1;
adultPairs = 0;
infantPairs = 1;
else
fibSequence = [0, 1];
for i = 3:n+1
fibSequence(i) = fibSequence(i-1) + fibSequence(i-2);
end
totalPairs = fibSequence(end);
adultPairs = fibSequence(end-1);
infantPairs = fibSequence(end-2);
end
end
```
In this function, we first handle the base cases of n = 0 and n = 1. Then, we calculate the Fibonacci sequence up to the nth term. Finally, we assign the values of totalPairs, adultPairs, and infantPairs based on the calculated Fibonacci sequence.
For example, if we call the function with n = 8, the output will be [21, 13, 8]. This means that in month 8, there would be a total of 21 pairs of rabbits, with 13 pairs being adult rabbits and 8 pairs being infant rabbits.
To know more about Fibonacci model refer to:
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