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A bacteria culture starts with 1 bacterium. Find a model for the bacteria population A after t hours under the given conditions. How do these models differ? (a) One bacterium is added to the population each hour. A(t) = (b) The population growth factor is 5. A(t) = (c) The population increases by 100% per hour. A(t) = (d) The population has an instantaneous growth rate of 1. A(t) =

A bacteria culture starts with 1 bacterium. Find a model for the bacteria population A after t hours under the given conditions. How do these models differ? (a) One bacterium is added to the population each hour. A(t) = (b) The population growth factor is 5. A(t) = (c) The population increases by 100% per hour. A(t) = (d) The population has an instantaneous growth rate of 1. A(t) =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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# Modeling Bacteria Population Growth A bacteria culture starts with 1 bacterium. Find a model for the bacteria population \( A \) after \( t \) hours under the given conditions. How do these models differ? ### (a) Linear Growth One bacterium is added to the population each hour. \[ A(t) = \] ### (b) Exponential Growth with Growth Factor The population growth factor is 5. \[ A(t) = \] ### (c) Exponential Growth with Percentage Increase The population increases by 100% per hour. \[ A(t) = \] ### (d) Continuous Growth The population has an instantaneous growth rate of 1. \[ A(t) = \] ### Explanation of Models - **Linear Growth (a):** Each hour, a fixed number of bacteria (one) is added, leading to a linear increase. - **Exponential Growth (b & c):** The population multiplies each hour, resulting in an exponential model. In (b), it multiplies by a factor of 5, while in (c), it doubles (100% increase) each hour. - **Continuous Growth (d):** The growth is continuous, modeled using a continuous growth rate, often expressed using the natural exponent \( e \). Understanding these models helps in analyzing different scenarios in bacterial population growth, reflecting linear and exponential changes over time.
Transcribed Image Text:# Modeling Bacteria Population Growth A bacteria culture starts with 1 bacterium. Find a model for the bacteria population \( A \) after \( t \) hours under the given conditions. How do these models differ? ### (a) Linear Growth One bacterium is added to the population each hour. \[ A(t) = \] ### (b) Exponential Growth with Growth Factor The population growth factor is 5. \[ A(t) = \] ### (c) Exponential Growth with Percentage Increase The population increases by 100% per hour. \[ A(t) = \] ### (d) Continuous Growth The population has an instantaneous growth rate of 1. \[ A(t) = \] ### Explanation of Models - **Linear Growth (a):** Each hour, a fixed number of bacteria (one) is added, leading to a linear increase. - **Exponential Growth (b & c):** The population multiplies each hour, resulting in an exponential model. In (b), it multiplies by a factor of 5, while in (c), it doubles (100% increase) each hour. - **Continuous Growth (d):** The growth is continuous, modeled using a continuous growth rate, often expressed using the natural exponent \( e \). Understanding these models helps in analyzing different scenarios in bacterial population growth, reflecting linear and exponential changes over time.
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