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Q4. (a) The pressure, P units, in a defective tyre, t hours after being inflated to a pressure of 50 units, is given by:

P = 50e- 0.01kt where k is a constant.

After 24 hours the tyre pressure falls to 40 units.

Calculate EACH of the following:

(i) the value of k, correct to 3 decimal places; (4)

(ii) the tyre pressure after 48 hours; (2)

(iii) the tyre pressure after 1 week. (2)

(b) Solve for x, x > 0, in the following equation: (8)

3^x2 = 27^x+1