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Q4. (a) A block of metal, initially at 0°C, is placed in a pre - heated oven set at 250°C.

The temperature of the metal, T°C, is given by the function T = 250(1^-ekt) where t is the time in minutes the metal has been in the oven and k is a constant.

Given that when t = 10, the temperature of the metal is 131.9℃, determine EACH of the following:

(i) The value of k

(ii) the temperature of the metal when t = 15.

b) Solve the following equation for x, stating the result correct to 3 decimal places:

In (1 - x³) = - 0.45

c) Transpose the following equation to make C the subject:

t = 1/M In (1/(1 + C))