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Q4. (a) The strike rate of ten - pin bowler will increase with practice and this can be approximated to the equation.

P = 100(t - 0.5^t )

where P is the percentage of strikes and t is the number of hours of practice per day.

Calculate EACH of the following:

(i) the number of hours of practice per day, (to the nearest hour), that are likely to be required to achieve a 90% strike rate; (5)

(ii) the likely strike rate, (to the nearest 1%), based on 6 hours practice per day. (3)

(b) Solve the following equation for x, correct to 2 decimal places: (8)

3^{x2- 1}= 9^2x