Question 3) A certain population of bacteria is known to grow at a rate proportional to the amount present in a culture that provides plentiful food and space. Initially, there are 40 bacteria, after seven hours 80 bacteria are observed in the culture. If so, (a) Find the constant of proportionality. (b) Find a mathematical expression that gives the number of bacteria present in the culture at time t. (c) Determine the number of bacteria that will be present in the culture after 42 hours.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 40E
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Question 3) A certain population of bacteria is known to grow at a rate proportional to the amount
present in a culture that provides plentiful food and space. Initially, there are 40 bacteria, after seven hours
80 bacteria are observed in the culture. If so,
(a) Find the constant of proportionality.
(b) Find a. mathematical expression that gives the number of bacteria present in the culture at
time t.
(c) Determine the number of bacteria that will be present in the culture after 42 hours.
Transcribed Image Text:Question 3) A certain population of bacteria is known to grow at a rate proportional to the amount present in a culture that provides plentiful food and space. Initially, there are 40 bacteria, after seven hours 80 bacteria are observed in the culture. If so, (a) Find the constant of proportionality. (b) Find a. mathematical expression that gives the number of bacteria present in the culture at time t. (c) Determine the number of bacteria that will be present in the culture after 42 hours.
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