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 = 0.5tcm, 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 2cm 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)How fast was the area of the disc increasing (cm2/hour) just before the antibiotic was introduced? (b) What was the maximum area of the disc? (c) 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 = 0.5tcm, 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 2cm 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)How fast was the area of the disc increasing (cm2/hour) just before the antibiotic was introduced?
(b) What was the maximum area of the disc?
(c) How fast was the area of the disc decreasing (cm2/hour) just as the disc disappeared due to the antibiotic?
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