Use Sage to program Exercise 5. In 1202 AD, Leonardo Pisano asked the following famous problem: A certain man had a pair of rabbits together in a certain enclosed place, and one wishes to know how many are created from the pair in one year when it is the nature for of them in a single month to bear another pair, and in the second month those born bear also. Because the abovewritten pair in the first month bore, you will double it. there will be two pairs in one month. One of these, namely the first, bears in the second month, and thus there are in the second month three pairs; of these in one month two are pregnant, and in the third month 2 pairs of rabbits are born, and thus there are 5 pairs in the month;... Explain how the rabbits reproduce. Create a list F where F[x] is the number of rabbits in month x. (so F[0]=1, F[1]=2) Find F[12]. Find F[100].
Use Sage to program
Exercise 5.
In 1202 AD, Leonardo Pisano asked the following famous problem:
A certain man had a pair of rabbits together in a certain enclosed
place, and one wishes to know how many are created from the pair in
one year when it is the nature for of them in a single month to bear
another pair, and in the second month those born bear also. Because
the abovewritten pair in the first month bore, you will double it. there
will be two pairs in one month. One of these, namely the first, bears in
the second month, and thus there are in the second month three pairs;
of these in one month two are pregnant, and in the third month 2
pairs of rabbits are born, and thus there are 5 pairs in the month;...
Explain how the rabbits reproduce. Create a list F where F[x] is the number of
rabbits in month x. (so F[0]=1, F[1]=2) Find F[12]. Find F[100].
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