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Q4. (a) The value £ V of a standby generator after t years is given by:

V = 95000 e^{- 0.226t}

The generator is to be replaced when its value falls to its scrap value of £ 10000.

Determine EACH of the following for the generator:

(i) It’s cost when new; (2)

(ii) Its value after 5 years; (2)

(iii) Its expected lifetime to the nearest year. (6)

(b) Solve the following equation for x:

2x² = 8^{2x - 3} (6)