A biochemist is testing the effect of a new antibiotic on a particular bacteria growing in a petri dish. Without the antibiotic the bacteria 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 bacteria was introduced to the petri dish. The area of the bacteria is given by A = πr2, the area of a disc of radius r. When the radius of the disc reaches 2 cm the biochemist introduces the antibiotic. This causes the radius of the disc to reduce according to r = 2 − √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 bacteria until its disappearance)? (b) Graph the radius of the disc against elapsed time since the start of the experiment. (c) How fast was the area of the disc increasing (cm2/hour) just before the antibiotic was introduced? (d) What was the maximum area of the disc? (e) How fast was the area of the disc decreasing (cm2/hour) just as the disc disappeared due to the antibiotic?
A biochemist is testing the effect of a new antibiotic on a particular bacteria growing in a petri dish. Without the antibiotic the bacteria 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 bacteria was introduced to the petri dish. The area of the bacteria is given by A = πr2, the area of a disc of radius r. When the radius of the disc reaches 2 cm the biochemist introduces the antibiotic. This causes the radius of the disc to reduce according to r = 2 − √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 bacteria until its disappearance)?
(b) Graph the radius of the disc against elapsed time since the start of the experiment.
(c) How fast was the area of the disc increasing (cm2/hour) just before the antibiotic was introduced?
(d) What was the maximum area of the disc?
(e) How fast was the area of the disc decreasing (cm2/hour) just as the disc disappeared due to the antibiotic?
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