Due primarily to irresponsible use of chemicals, otter population in a country declined dramatically during the twentieth century until otters could be found on only a small percentage of riverbanks. After chemical bans were put in place, the number of riverside sites R(t) occupied by otters rose significantly and can be approximated by the exponential function, R(t) = 293(1.067), where t is the number of years since 1985. a) How many riverbanks were occupied by otters in 2012? b) In what year were there otters on 1000 riverbanks? c) What is the doubling time for the number riverbanks occupied by otters?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
parts a-c
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