Question 1

Paper 1, no calculatorEasy5 marks

The concentration CC in mg L−1\text{mg L}^{-1} of a dye in a tank tt hours after treatment begins is modelled by

C(t)=32(14)t.C(t)=32\left(\frac14\right)^t.
(a)

Find the concentration after 32\frac32 hours.

[2]
(b)

Determine the time at which the concentration reaches 3 mg L−13\text{ mg L}^{-1} Use logarithms and give your answer exactly in terms of ln⁡\ln including units.

[3]

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