(a) Find an expression for the number of bacteria after t hours. (Round your numeric values to four decimal places.) P(t) = (b) Find the number of bacteria after 4 hours. (Round your answer to the nearest whole number.) P(4) = bacteria (c) Find the rate of growth (in bacteria per hour) after 4 hours. (Round your answer to the nearest whole number.) P'(4)= bacteria per hour (d) After how many hours will the population reach 250,000? (Round your answer to one decimal place.) hr
(a) Find an expression for the number of bacteria after t hours. (Round your numeric values to four decimal places.) P(t) = (b) Find the number of bacteria after 4 hours. (Round your answer to the nearest whole number.) P(4) = bacteria (c) Find the rate of growth (in bacteria per hour) after 4 hours. (Round your answer to the nearest whole number.) P'(4)= bacteria per hour (d) After how many hours will the population reach 250,000? (Round your answer to one decimal place.) hr
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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Q2. Please answer all the parts to this question

Transcribed Image Text:A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into a nutrient broth, the culture grows at a rate proportional to its size. After 1.5 hours, the population has increased to 825.
(a) Find an expression for the number of bacteria after t hours. (Round your numeric values to four decimal places.)
P(t) =
(b) Find the number of bacteria after 4 hours. (Round your answer to the nearest whole number.)
P(4) =
bacteria
(c) Find the rate of growth (in bacteria per hour) after 4 hours. (Round your answer to the nearest whole number.)
P'(4)=
bacteria per hour
(d) After how many hours will the population reach 250,000? (Round your answer to one decimal place.)
t =
hr
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