Homework: Ho A strain of bacteria is placed into a petri dish at 30°C and allowed to grow. The following data are collected. Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth. The population is measured using an optical device in which the amount of light that passes through the petri dish is measured. Complete parts (a)-(e) Time (hours), x Population, y 0 0.16 0.31 0.44 0.58 0.82 5555 (a) Treating time, x, as the predictor variable, use a graphing utility to fit an exponential function to the data. y=ab*= (Round to four decimal places as needed.)
Homework: Ho A strain of bacteria is placed into a petri dish at 30°C and allowed to grow. The following data are collected. Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth. The population is measured using an optical device in which the amount of light that passes through the petri dish is measured. Complete parts (a)-(e) Time (hours), x Population, y 0 0.16 0.31 0.44 0.58 0.82 5555 (a) Treating time, x, as the predictor variable, use a graphing utility to fit an exponential function to the data. y=ab*= (Round to four decimal places as needed.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Homework: Homework 7**
**Problem Statement:**
A strain of bacteria is placed into a petri dish at 30°C and allowed to grow. The following data are collected. Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth. The population is measured using an optical device in which the amount of light that passes through the petri dish is measured. Complete parts (a)-(c).
| Time (hours), x | Population, y |
|-----------------|----------------|
| 0 | 0.16 |
| 2.5 | 0.31 |
| 3.5 | 0.44 |
| 4.5 | 0.58 |
| 6 | 0.82 |
**Part (a):**
Treating time, \( x \), as the predictor variable, use a graphing utility to fit an exponential function to the data.
**Exponential Function:**
\[ y = ab^x \]
(Round to four decimal places as needed.)
**Additional Resources:**
- View an example
- Textbook
**Interactive Elements:**
- Clear all
- Check answer](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F532926f3-4b43-4cc7-9179-861836f9d644%2F34019154-9694-4dcd-a483-632b65ae48b3%2F98303a9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Homework: Homework 7**
**Problem Statement:**
A strain of bacteria is placed into a petri dish at 30°C and allowed to grow. The following data are collected. Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth. The population is measured using an optical device in which the amount of light that passes through the petri dish is measured. Complete parts (a)-(c).
| Time (hours), x | Population, y |
|-----------------|----------------|
| 0 | 0.16 |
| 2.5 | 0.31 |
| 3.5 | 0.44 |
| 4.5 | 0.58 |
| 6 | 0.82 |
**Part (a):**
Treating time, \( x \), as the predictor variable, use a graphing utility to fit an exponential function to the data.
**Exponential Function:**
\[ y = ab^x \]
(Round to four decimal places as needed.)
**Additional Resources:**
- View an example
- Textbook
**Interactive Elements:**
- Clear all
- Check answer
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