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The small intestine bacteria, while inhabiting areas optimal for growth, have a doubling time of roughly 10 hours. A normal small intestine starting population would be approximately 10, 000 bacteria per ml of fluid. Write an equation to model this exponential growth, with b(x) representing the number of bacteria per ml and x representing the time in hours.

The small intestine bacteria, while inhabiting areas optimal for growth, have a doubling time of roughly 10 hours. A normal small intestine starting population would be approximately 10, 000 bacteria per ml of fluid. Write an equation to model this exponential growth, with b(x) representing the number of bacteria per ml and x representing the time in hours.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The small intestine bacteria, while inhabiting areas optimal for growth, have a doubling time of roughly 10 hours. A normal small intestine starting population would be approximately 10, 000 bacteria per ml of fluid. Write an equation to model this exponential growth, with b(x) representing the number of bacteria per ml and x representing the time in hours. a) b) How long will it take for there to be 100, 000 bacteria per ml? (Round your answer to two decimal places if necessary) e) Determine the average rate ofchange between 20 hours and 30 hours. f) Estimate the instantaneous rate of change at 24 hours.
Transcribed Image Text:The small intestine bacteria, while inhabiting areas optimal for growth, have a doubling time of roughly 10 hours. A normal small intestine starting population would be approximately 10, 000 bacteria per ml of fluid. Write an equation to model this exponential growth, with b(x) representing the number of bacteria per ml and x representing the time in hours. a) b) How long will it take for there to be 100, 000 bacteria per ml? (Round your answer to two decimal places if necessary) e) Determine the average rate ofchange between 20 hours and 30 hours. f) Estimate the instantaneous rate of change at 24 hours.
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