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 hasincreased to 775.(a) Find an expression for the number of bacteria after t hours. (Round your numeric values to four decimal places.)P(E) = 50(6.2166)'%3D(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

Given: Initial population = 50. After 1.5 hours, the population size = 775. Given that the bacteria…

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 775.

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 775.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 13EQ

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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 775.
(a) Find an expression for the number of bacteria after t hours. (Round your numeric values to four decimal places.)
P(E) = 50(6.2166)'
%3D
(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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