Calculate the number of tablets Ethel has to receive for a complete course of promethazine 12.5mg bd for 3 days, given that the stock available is 25mg tablets.

Q(a)

Step 1: Formula for amount of drug remaining.

$A = A_0 \left( \frac{1}{2} \right)^{t / t_{1/2}}$

Step 2: Substitute given values ($A_0 = 12$ mg, $t = 5$ h, $t_{1/2} = 10$ h).

$A = 12 \left( \frac{1}{2} \right)^{5/10}$

Step 3: Simplify exponent.

$A = 12 \left( \frac{1}{2} \right)^{0.5} = 12 \times 2^{-0.5}$

Step 4: Calculate $2^{0.5} = \sqrt{2} \approx 1.414$.

$2^{-0.5} = \frac{1}{1.414} \approx 0.707$

Step 5: Multiply.

$A \approx 12 \times 0.707 = 8.5 mg$

Final answer: 8.5 \text{ mg}

Q(b)

Step 1: Formula for mass of insulin.

$m = \frac{U}{c}$

where $U$ is units, $c = 28.8$ units/mg.

Step 2: Substitute $U = 35$ units.

$m = \frac{35}{28.8}$

Step 3: Divide.

$28.8 \times 1.2 = 34.56$

$35 - 34.56 = 0.44$

$0.44 / 28.8 \approx 0.015$

$m \approx 1.2 + 0.015 = 1.22 mg$

Final answer: 1.22 \text{ mg}

Q(c)

Step 1: Number of doses per day.

$\frac{24 h}{6 h/dose} = 4 doses/day$

Step 2: Tablets per dose (500 mg dose, 500 mg/tablet).

$1 tablet/dose$

Step 3: Total tablets per day.

$4 doses/day \times 1 tablet/dose = 4 tablets/day$

Final answer: 4 \text{ tablets/day}