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 925. (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 5 hours. (Round your answer to the nearest whole number.) P(5) =___bacteria (c) Find the rate of growth (in bacteria per hour) after 5 hours. (Round your answer to the nearest whole number.) P ′(5)=___bacteria per hour (d) After how many hours will the population reach 250,000? (Round your answer to one decimal place.)
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 925. (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 5 hours. (Round your answer to the nearest whole number.) P(5) =___bacteria (c) Find the rate of growth (in bacteria per hour) after 5 hours. (Round your answer to the nearest whole number.) P ′(5)=___bacteria per hour (d) After how many hours will the population reach 250,000? (Round your answer to one decimal place.)
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter7: Applying Fractions
Section7.9: Negative Exponents
Problem 25OE
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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 925.
(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 5 hours. (Round your answer to the nearest whole number.)
P(5) =___bacteria
(c)
Find the rate of growth (in bacteria per hour) after 5 hours. (Round your answer to the nearest whole number.)
P ′(5)=___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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