Consider the following situation. A problem dating back to the early 13th century, posed by Leonardo Fibonacc…

Consider the following situation. A problem dating back to the early 13th century, posed by Leonardo Fibonacci, asks how many rabbits you would have if you started with one pair and let them reproduce. Assume that a pair of rabbits produces a pair of offspring each month, and that each pair of rabbits produces their first offspring at the age of $2$ months. Month by month, the number of pairs of rabbits is given by the sum of the pairs in the two preceding months, except for the $0$th and the $1$st months. The table alongside lists the number of pairs for months $0$ to $16$; after about $16$ months you have nearly $1600$ pairs of rabbits. Clearly state the problem and the different stages of mathematical modelling in this situation.