1. A sum of $1000 is invested in a bank account that pays 10% compound interest monthly. The amount of money y in the account after t months is modelled by the equation y = ka where k>0 and a > 0. (a) What are the values of k and a? Show all of your working. (b) How much money is in the account after 2 months? Assuming that these two months consist of exactly 60 days, what is the average amount of money paid per day? (c} How long will it take for the account balance to be $2000? Leave your answer in exact form. (d) Sketch the graph of y = ka'. Include the y-intercept and the point (1, ka), using the %3D Dart (a)

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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.