A biochemist is testing the effect of a new antibiotic on a particular
mould growing in a petri dish. Without the antibiotic the mould grows as a
circular patch with the radius increasing with time according to r = 0.5t cm
where t is measured in hours since the mould was introduced to the petri dish.
The area of the mould is given by A = pr2
, the area of a disc of radius r. When
the radius of the disc reaches 2cm the biochemist introduces the antibiotic. This
causes the radius of the disc to reduce according to r = 2 –
v
t cm where t is
measured in hours since the antibiotic was introduced.
(a) What was the time duration of the entire experiment (from the introduction of the mould until its disappearance)? [3 marks]
(b) Graph the radius of the disc against elapsed time since the start of the
experiment. [3 marks]
(c) How fast was the area of the disc increasing (cm2
/hour) just before the
antibiotic was introduced? [3 marks]
(d) What was the maximum area of the disc? [3 marks]
(e) How fast was the area of the disc decreasing (cm2
/hour) just as the disc
disappeared due to the antibiotic? [3 marks]