(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
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Q2. Please answer all the parts to this question 

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
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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