The number of bacteria in a culture is given by the function n(t) = 945e0.4t where t is measured in hours. (a) What is the relative rate of growth of this bacterium population? Your answer is percent (b) What is the initial population of the culture (at t=0)? Your answer is (c) How many bacteria will the culture contain at time t=5? Your answer is
The number of bacteria in a culture is given by the function n(t) = 945e0.4t where t is measured in hours. (a) What is the relative rate of growth of this bacterium population? Your answer is percent (b) What is the initial population of the culture (at t=0)? Your answer is (c) How many bacteria will the culture contain at time t=5? Your answer is
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 11DE
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Question
![### Bacterial Growth in a Culture: Exponential Model
The growth of bacteria in a culture can be modeled by the exponential function:
\[ n(t) = 945e^{0.4t} \]
where \( t \) is measured in hours.
#### Questions and Answers
1. **What is the relative rate of growth of this bacterium population?**
- The relative rate of growth is determined by the exponent in the exponential function. In this case, the exponent is \( 0.4 \).
- **Answer**: \(\_\_\_\_\_\_\_\_\_\_) percent
2. **What is the initial population of the culture (at \( t = 0 \))?**
- To find the initial population, substitute \( t = 0 \) into the function:
\[ n(0) = 945e^{0.4 \times 0} = 945e^{0} = 945 \]
- **Answer**: \(\_\_\_\_\_\_\_\_\_\_\)
3. **How many bacteria will the culture contain at time \( t = 5 \)?**
- To calculate the population at \( t = 5 \) hours, substitute \( t = 5 \) into the function:
\[ n(5) = 945e^{0.4 \times 5} = 945e^{2} \]
- This requires evaluating the expression \( e^2 \) and then multiplying by 945.
- **Answer**: \(\_\_\_\_\_\_\_\_\_\_\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6df536a0-f13a-4341-a0f7-2359bab40649%2F7108bb8b-6dd5-4239-8971-57d65ffaaa95%2Fjxvpzgq_processed.png&w=3840&q=75)
Transcribed Image Text:### Bacterial Growth in a Culture: Exponential Model
The growth of bacteria in a culture can be modeled by the exponential function:
\[ n(t) = 945e^{0.4t} \]
where \( t \) is measured in hours.
#### Questions and Answers
1. **What is the relative rate of growth of this bacterium population?**
- The relative rate of growth is determined by the exponent in the exponential function. In this case, the exponent is \( 0.4 \).
- **Answer**: \(\_\_\_\_\_\_\_\_\_\_) percent
2. **What is the initial population of the culture (at \( t = 0 \))?**
- To find the initial population, substitute \( t = 0 \) into the function:
\[ n(0) = 945e^{0.4 \times 0} = 945e^{0} = 945 \]
- **Answer**: \(\_\_\_\_\_\_\_\_\_\_\)
3. **How many bacteria will the culture contain at time \( t = 5 \)?**
- To calculate the population at \( t = 5 \) hours, substitute \( t = 5 \) into the function:
\[ n(5) = 945e^{0.4 \times 5} = 945e^{2} \]
- This requires evaluating the expression \( e^2 \) and then multiplying by 945.
- **Answer**: \(\_\_\_\_\_\_\_\_\_\_\)
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