The amount of water, A, in thousands of litres, available in a water tank located on a farm fluctuates in a yearly cycle and can be modelled by the function A(t) = a sin (kt) + b, where t is the elapsed time, in weeks, since the start of the year. The amount of water available in the tank on week 6 is 24 thousand litres and on week 31 is 9.2 thousand litres. (a) Find the value of k, in degrees, assuming there are 52 whole weeks in a year. (b) Set up a pair of equations to find the value of a and the value of b. Give your answers correct to the nearest integer. (c) Hence find the

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