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1. 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 = r², 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) What was the time duration of the entire experiment (from the introduc- tion of the mould 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?

1. 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 = r², 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) What was the time duration of the entire experiment (from the introduc- tion of the mould 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?

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
Section: Chapter Questions
Problem 44AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...
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1. 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 = r², 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) What was the time duration of the entire experiment (from the introduc- tion of the mould 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?
Transcribed Image Text:1. 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 = r², 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) What was the time duration of the entire experiment (from the introduc- tion of the mould 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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