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
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Chapter1: Functions And Models
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42702b25-0167-42f0-be60-3271d8dbb54a%2F4652d623-87d7-4b1d-bd07-e04179419de7%2Fsshms1n_processed.png&w=3840&q=75)
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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