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. y 700 600 500 Number of yeast cells 400 300 200 100 0 0 2 4 6 8 12 14 16 18 Time (in hours) I (a) Describe how the rate of population increase varies. 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 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 initially very small, then gets larger until it reaches a maximum at about t = 18 hours. O The rate of increase of the population is consistently small. O The rate of increase of the population is consistently large. (b) At what point is the rate of population increase the highest? (t, y) = (c) On what interval(s) is the population function concave upward? (Enter your answer using interval notation.) On what interval(s) is the population function concave downward? (Enter your answer using interval notation.)
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. y 700 600 500 Number of yeast cells 400 300 200 100 0 0 2 4 6 8 12 14 16 18 Time (in hours) I (a) Describe how the rate of population increase varies. 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 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 initially very small, then gets larger until it reaches a maximum at about t = 18 hours. O The rate of increase of the population is consistently small. O The rate of increase of the population is consistently large. (b) At what point is the rate of population increase the highest? (t, y) = (c) On what interval(s) is the population function concave upward? (Enter your answer using interval notation.) On what interval(s) is the population function concave downward? (Enter your answer using interval notation.)
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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Transcribed Image Text: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.
y
700
600
500
Number of
yeast cells 400
300
200
100
0
0
2
4
6
8 12 14 16 18
Time (in hours)
(a) Describe how the rate of population increase varies.
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 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 initially very small, then gets larger until it reaches a maximum at about t = 18 hours.
O The rate of increase of the population is consistently small.
O The rate of increase of the population is consistently large.
(b) At what point is the rate of population increase the highest?
(t, y) =
I
(c) On what interval(s) is the population function concave upward? (Enter your answer using interval notation.)
On what interval(s) is the population function concave downward? (Enter your answer using interval notation.)
(d) Estimate the coordinates of the inflection point.
(t₁ y) =
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