A graph of a population of yeast cells in a new laboratory culture as a function of time from t = 0 to t = 18 is shown. 700 600 500 Number of 400 yeast cells 300 200 100 4 8 10 12 14 16 18 Time (in hours) (a) Describe how the rate of population increase varies. The rate of increase of the population is initially very small, then gets larger until it reaches a maximum at abou t = 8 hours, and decreases toward 0 as the population begins to level off. The rate of increase of the population is initially very small, then gets larger until it reaches a maximum at abou t = 18 hours. The rate of increase of the population is initially very large, then gets smaller until it reaches a minimum at abo t = 8 hours, and increases toward 0 as the population begins to level off. The rate of increase of the population is consistently large. O The rate of increase of the population is consistently small. (b) At what point is the rate of population increase the greatest? (t, y) = (c) On what interval is the population function concave upward? (Enter your answer using interval notation.) On what interval is the population function concave downward? (Enter your answer using interval notation.) (d) Estimate the coordinates of the inflection point. (t, y) =
A graph of a population of yeast cells in a new laboratory culture as a function of time from t = 0 to t = 18 is shown. 700 600 500 Number of 400 yeast cells 300 200 100 4 8 10 12 14 16 18 Time (in hours) (a) Describe how the rate of population increase varies. The rate of increase of the population is initially very small, then gets larger until it reaches a maximum at abou t = 8 hours, and decreases toward 0 as the population begins to level off. The rate of increase of the population is initially very small, then gets larger until it reaches a maximum at abou t = 18 hours. The rate of increase of the population is initially very large, then gets smaller until it reaches a minimum at abo t = 8 hours, and increases toward 0 as the population begins to level off. The rate of increase of the population is consistently large. O The rate of increase of the population is consistently small. (b) At what point is the rate of population increase the greatest? (t, y) = (c) On what interval is the population function concave upward? (Enter your answer using interval notation.) On what interval is the population function concave downward? (Enter your answer using interval notation.) (d) Estimate the coordinates of the inflection point. (t, y) =
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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![This graph illustrates the population of yeast cells in a new laboratory culture over time, from \( t = 0 \) to \( t = 18 \) hours.
### Graph Description:
- **X-axis (horizontal):** Represents time in hours.
- **Y-axis (vertical):** Represents the number of yeast cells.
- **Curve:** Initially, the curve rises slowly, steepens to reach a peak around \( t = 8 \) hours, and then the growth slows down, indicating the population leveling off.
### Questions and Answers:
(a) **Describe how the rate of population increase varies.**
- **Correct Option:**
- The rate of increase of the population is initially very small, then gets larger until it reaches a maximum at about \( t = 8 \) hours, and decreases toward 0 as the population begins to level off.
(b) **At what point is the rate of population increase the greatest?**
- \((t, y) = \) [A space for users to fill in the answer]
(c) **On what interval is the population function concave upward?**
- [A space for users to enter the interval]
**On what interval is the population function concave downward?**
- [A space for users to enter the interval]
(d) **Estimate the coordinates of the inflection point.**
- \((t, y) = \) [A space for users to fill in the answer]
### Instructions:
- Use the graph to determine the precise times and coordinates for the maximum rate of increase and the inflection point, and enter your answers in the spaces provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61d3fec5-12f7-45ef-a221-7ede5a9d6496%2F4b8b5df8-e606-4715-a7e5-e786df4affd7%2Fn0qvjtc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:This graph illustrates the population of yeast cells in a new laboratory culture over time, from \( t = 0 \) to \( t = 18 \) hours.
### Graph Description:
- **X-axis (horizontal):** Represents time in hours.
- **Y-axis (vertical):** Represents the number of yeast cells.
- **Curve:** Initially, the curve rises slowly, steepens to reach a peak around \( t = 8 \) hours, and then the growth slows down, indicating the population leveling off.
### Questions and Answers:
(a) **Describe how the rate of population increase varies.**
- **Correct Option:**
- The rate of increase of the population is initially very small, then gets larger until it reaches a maximum at about \( t = 8 \) hours, and decreases toward 0 as the population begins to level off.
(b) **At what point is the rate of population increase the greatest?**
- \((t, y) = \) [A space for users to fill in the answer]
(c) **On what interval is the population function concave upward?**
- [A space for users to enter the interval]
**On what interval is the population function concave downward?**
- [A space for users to enter the interval]
(d) **Estimate the coordinates of the inflection point.**
- \((t, y) = \) [A space for users to fill in the answer]
### Instructions:
- Use the graph to determine the precise times and coordinates for the maximum rate of increase and the inflection point, and enter your answers in the spaces provided.
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