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Q4) (a) The pressure in a particular life raft falls according to the formula P_t = P_o e^-kt

Where P_o is the initial pressure, P_t is the pressure t hours after inflation and k is a constant.

When t = 0, the initial pressure is 100 units.

After 15 hours the pressure was 70 units.

If the pressure falls to 50 units or less, the raft is deemed unsafe.

Calculate EACH of the following for the raft:

(i) the value of k, correct to 3 decimal places; (5)

(ii) the safe lifetime in hours, to the nearest hour, assuming the pressure is not topped up. (5)

(b) Calculate the value of x, correct to 3 decimal places, such that

log_e (2 - 1/x) = - 0.3 (6)