Write down the number of bacteria in the colony at time $t = 0$.

Calculate the number of bacteria present at 2 hours and 30 minutes. Give your answer correct to the nearest hundred bacteria.

Calculate the time, in hours, for the number of bacteria to reach 5500.

800     (A1)     (C1)

$800 \times {3^{(0.5 \times 2.5)}}$     (M1)

Note: Award (M1) for correctly substituted formula.

$= 3158.57$...     (A1)

$= 3200$     (A1)     (C3)

Notes: Final (A1) is given for correctly rounding their answer. This may be awarded regardless of a preceding (A0).

$5500 = 800 \times {3^{(0.5 \times t)}}$     (M1)

Notes: Award (M1) for equating function to 5500. Accept correct alternative methods.

$= 3.51{\text{ hours}}$ (3.50968...)     (A1)     (C2)