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Q4. (a) Determine the value of x, for x > 0, which satisfies EACH of the following equations:

(i) ln (5 - 2x³) = -0.8    (4)

(ii) x^7.5 = (2x)³          (4)

(b) The pressure in a particular life raft falls according to the formula:

P_t = P₀ e^-kt Where P₀ is the initial pressure at time t hours and k is a constant.

(i) When t = 0 the pressure is 80 units and 12 hours later it is 60 units.

Calculate the value of k to two significant figures. (4)

(ii) When the pressure falls below 40 units the raft is unsafe.

Calculate the length of time the raft is safe to use. (4)