a) To write down two equations in \( p \) and \( q \):
At \( t = 0 \) (12:00): \( C = 47 \)
\( p \times 2^{0.5 \times 0} + q = p + q = 47 \)

At \( t = 4 \) (16:00): \( C = 53 \)
\( p \times 2^{0.5 \times 4} + q = p \times 2^2 + q = 4p + q = 53 \)

Thus:
\( p + q = 47 \), \( 4p + q = 53 \) [2]

b) To calculate the values of \( p \) and \( q \):
Solve the system:
\( p + q = 47 \)
\( 4p + q = 53 \)

Subtract: \( (4p + q) – (p + q) = 53 – 47 \)
\( 3p = 6 \)
\( p = 2 \)

Substitute \( p = 2 \) into \( p + q = 47 \):
\( 2 + q = 47 \)
\( q = 45 \)

Thus:
\( p = 2 \), \( q = 45 \) [2]

c) To find the number of cells at 22:00 (\( t = 10 \)):
Substitute \( p = 2 \), \( q = 45 \), \( t = 10 \):
\( C = 2 \times 2^{0.5 \times 10} + 45 = 2 \times 2^5 + 45 \)
\( = 2 \times 32 + 45 = 64 + 45 = 109 \)

Thus:
The number of cells is \( 109 \) [2]