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 6 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 about t = 8 hours, and decreases toward 0 as the population begins to level off. O The rate of increase of the population is consistently large. O The rate of increase of the population is initially very large, then gets smaller until it reaches a minimum at about t = 8 hours, and increases toward 0 as the population begins to level off. O The rate of increase of the population is consistently small. The rate of increase of the population is initially very small, then gets larger until it reaches a maximum at about t = 18 hours. (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 6 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 about t = 8 hours, and decreases toward 0 as the population begins to level off. O The rate of increase of the population is consistently large. O The rate of increase of the population is initially very large, then gets smaller until it reaches a minimum at about t = 8 hours, and increases toward 0 as the population begins to level off. O The rate of increase of the population is consistently small. The rate of increase of the population is initially very small, then gets larger until it reaches a maximum at about t = 18 hours. (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
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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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![### Population Growth Analysis of Yeast Cells
#### Graph Explanation:
The graph depicts the population of yeast cells in a laboratory culture over a period from \( t = 0 \) to \( t = 18 \) hours. The y-axis represents the "Number of yeast cells," ranging from 0 to 700, while the x-axis represents "Time (in hours)."
The curve starts at the low number of yeast cells and increases rapidly, reaches a peak growth rate, and then levels off, indicating slower growth as resources or space become limited.
#### Questions and Answers:
(a) **Describe how the rate of population increase varies.**
- The population growth rate is initially very small, increases until a maximum at \( t \approx 8 \) hours, then decreases toward zero as the population begins to level off.
Options:
- ◯ 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.
- ◯ The rate of increase of the population is consistently large.
- ◯ The rate of increase of the population is initially very large, then gets smaller until it reaches a minimum at about \( t = 8 \) hours, and increases toward 0 as the population begins to level off.
- ◯ The rate of increase of the population is consistently small.
- ◯ The rate of increase of the population is initially very small, then gets larger until it reaches a maximum at about \( t = 18 \) hours.
(b) **At what point is the rate of population increase the greatest?**
\[
(t, y) = (\text{\_\_\_\_})
\]
(c) **On what interval is the population function concave upward?**
\[
\text{Interval: (\_\_\_\_, \_\_\_\_)}
\]
**On what interval is the population function concave downward?**
\[
\text{Interval: (\_\_\_\_, \_\_\_\_)}
\]
(d) **Estimate the coordinates of the inflection point.**
\[
(t, y) = (\text{\_\_\_\_})
\]
This exercise helps in understanding the different phases of population growth including lag, exponential, and stationary phases, often found in biological cultures.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F933f1d50-b8af-4263-b716-1a2a3e9af3ea%2Fcebfea63-e74e-4e73-874b-335a7686abe9%2F9gzvuch_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Population Growth Analysis of Yeast Cells
#### Graph Explanation:
The graph depicts the population of yeast cells in a laboratory culture over a period from \( t = 0 \) to \( t = 18 \) hours. The y-axis represents the "Number of yeast cells," ranging from 0 to 700, while the x-axis represents "Time (in hours)."
The curve starts at the low number of yeast cells and increases rapidly, reaches a peak growth rate, and then levels off, indicating slower growth as resources or space become limited.
#### Questions and Answers:
(a) **Describe how the rate of population increase varies.**
- The population growth rate is initially very small, increases until a maximum at \( t \approx 8 \) hours, then decreases toward zero as the population begins to level off.
Options:
- ◯ 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.
- ◯ The rate of increase of the population is consistently large.
- ◯ The rate of increase of the population is initially very large, then gets smaller until it reaches a minimum at about \( t = 8 \) hours, and increases toward 0 as the population begins to level off.
- ◯ The rate of increase of the population is consistently small.
- ◯ The rate of increase of the population is initially very small, then gets larger until it reaches a maximum at about \( t = 18 \) hours.
(b) **At what point is the rate of population increase the greatest?**
\[
(t, y) = (\text{\_\_\_\_})
\]
(c) **On what interval is the population function concave upward?**
\[
\text{Interval: (\_\_\_\_, \_\_\_\_)}
\]
**On what interval is the population function concave downward?**
\[
\text{Interval: (\_\_\_\_, \_\_\_\_)}
\]
(d) **Estimate the coordinates of the inflection point.**
\[
(t, y) = (\text{\_\_\_\_})
\]
This exercise helps in understanding the different phases of population growth including lag, exponential, and stationary phases, often found in biological cultures.
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