You prescribe an antibiotic to a patient to cure an infection. We know that the rate of change of bacteria population is proportional to the amount left. Let P(t) represent the population of the bacteria. dP dt (a) Write a differential equation for Use k as your constant of proportionality. dP dt . (b) Solve the differential equation given that originally there approximately 210 bacteria in the petri dish, but 18 hours later, there were approximately 270 bacteria.
You prescribe an antibiotic to a patient to cure an infection. We know that the rate of change of bacteria population is proportional to the amount left. Let P(t) represent the population of the bacteria. dP dt (a) Write a differential equation for Use k as your constant of proportionality. dP dt . (b) Solve the differential equation given that originally there approximately 210 bacteria in the petri dish, but 18 hours later, there were approximately 270 bacteria.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:You prescribe an antibiotic to a patient to cure an infection.
We know that the rate of change of bacteria population is proportional to the amount
left. Let P(t) represent the population of the bacteria.
dP
(a) Write a differential equation for Use k as your constant of proportionality.
dt
dP
dt
=
(b) Solve the differential equation given that originally there approximately 210 bacteria
in the petri dish, but 18 hours later, there were approximately 270 bacteria.
P(t)
=
(c) How many bacteria can we expect to have after 35 hours? Round to the nearest
whole number.
bacteria
(d) When are there approximately 1100 bacteria? Round to three decimal places.
hours
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