In the 14th century, an Indian mathematician named Narayana wondered what would happen if the ability of a cow to reproduce was delayed. Suppose each cow produces one female calf each year beginning in its fourth year, at which time it is considered an adult. Suppose we begin with one female calf in its first year and none die.
a. What is the total number of cows and calves for each of the first 11 years?
b. How many adult cows are there each year for each of the first 11 years?
c. How many calves are there each year for each of the first 11 years?
d. While the total number of cows and calves each year does not form a Fibonacci sequence, a similar recursion rule will generate the sequence. Find the rule and predict the number of cows and calves in each of the years 12 through 16.
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