A bacterial infection in an internal wound grows as , where the time is in hours. A dose of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population

Question

A bacterial infection in an internal wound grows as , where the time  is in hours. A dose of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population goes down as . What will be the plot of  vs  after 1 hour?

Canvas Classes · Accepted Answer

After 1 hour, the antibiotic reaches the wound. At , .

For :  (second order decay)

Integrating:  where

This is a linear function of  (for ), starting at  at  and increasing linearly.

The plot of  vs  is a straight line with positive slope starting from a value less than 1 at .

Answer: Option (3)

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