Calculus (MindTap Course List)
8th Edition
ISBN: 9781285740621
Author: James Stewart
Publisher: Cengage Learning
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Chapter 9.4, Problem 8E
The table gives the number of yeast cells in a new laboratory culture.
| Time (hours) | Yeast cells |
| 0 | 18 |
| 2 | 39 |
| 4 | 80 |
| 6 | 171 |
| 8 | 336 |
| 10 | 509 |
| 12 | 597 |
| 14 | 640 |
| 16 | 664 |
| 18 | 672 |
(a) Plot the data and use the plot to estimate the carrying capacity for the yeast population.
(b) Use the data to estimate the initial relative growth rate.
(c) Find both an exponential model and a logistic model for these data.
(d) Compare the predicted values with the observed values, both in a table and with graphs. Comment on how well your models fit the data.
(e) Use your logistic model to estimate the number of yeast cells after 7 hours.
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Chapter 9 Solutions
Calculus (MindTap Course List)
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Brine that...Ch. 9.3 - Prob. 49ECh. 9.3 - An object of mass m is moving horizontally through...Ch. 9.3 - Prob. 51ECh. 9.3 - Prob. 52ECh. 9.3 - Let A(t) be the area of a tissue culture at time t...Ch. 9.3 - Prob. 54ECh. 9.4 - 12 A population grows according to the given...Ch. 9.4 - 1-2 A population grows according to the given...Ch. 9.4 - Suppose that a population develops according to...Ch. 9.4 - Suppose that a population grows according to a...Ch. 9.4 - The Pacific halibut fishery has been modeled by...Ch. 9.4 - Suppose a population P(t) satisfies...Ch. 9.4 - Suppose a population grows according to a logistic...Ch. 9.4 - The table gives the number of yeast cells in a new...Ch. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - One model for the spread of a rumor is that the...Ch. 9.4 - Biologists stocked a lake with 400 fish and...Ch. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - Consider a population P=P(t) with constant...Ch. 9.4 - Let c be a positive number. A differential...Ch. 9.4 - Lets modify the logistic differential equation of...Ch. 9.4 - Consider the differential equation...Ch. 9.4 - There is considerable evidence to support the...Ch. 9.4 - Prob. 22ECh. 9.4 - In a seasonal-growth model, a periodic function of...Ch. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.5 - 14 Determine whether the differential equation is...Ch. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - 514 Solve the differential equation. y+y=1Ch. 9.5 - 514 Solve the differential equation. yy=exCh. 9.5 - 514 Solve the differential equation. y=xyCh. 9.5 - 514 Solve the differential equation....Ch. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - Prob. 13ECh. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - 1520 Solve the initial-value problem....Ch. 9.5 - Prob. 20ECh. 9.5 - Prob. 21ECh. 9.5 - Prob. 22ECh. 9.5 - A Bernoulli differential equation named after...Ch. 9.5 - 2425 Use the method of Exercise 23 to solve the...Ch. 9.5 - Prob. 25ECh. 9.5 - Prob. 26ECh. 9.5 - Prob. 27ECh. 9.5 - Prob. 28ECh. 9.5 - Prob. 29ECh. 9.5 - Prob. 30ECh. 9.5 - Prob. 31ECh. 9.5 - Prob. 32ECh. 9.5 - In Section 9.3 we looked at mixing problems in...Ch. 9.5 - Prob. 34ECh. 9.5 - An object with mass m is dropped from rest and we...Ch. 9.5 - If we ignore air resistance, we can conclude that...Ch. 9.5 - Prob. 37ECh. 9.5 - To account for seasonal variation in the logistic...Ch. 9.6 - For each predator-prey system, determine which of...Ch. 9.6 - Each system of differential equations is a model...Ch. 9.6 - Prob. 3ECh. 9.6 - Prob. 4ECh. 9.6 - 56 A phase trajectory is shown for populations of...Ch. 9.6 - 56 A phase trajectory is shown for populations of...Ch. 9.6 - 78 Graphs of populations of two species are shown....Ch. 9.6 - Prob. 8ECh. 9.6 - Prob. 9ECh. 9.6 - Populations of aphids and ladybugs are modeled by...Ch. 9.6 - In Example 1 we used Lotka-Volterra equations to...Ch. 9.6 - In Exercise 10 we modeled populations of aphids...Ch. 9.R - Prob. 1CCCh. 9.R - Prob. 2CCCh. 9.R - Prob. 3CCCh. 9.R - Prob. 4CCCh. 9.R - Prob. 5CCCh. 9.R - Prob. 6CCCh. 9.R - Prob. 7CCCh. 9.R - Prob. 8CCCh. 9.R - a Write Lotka-Volterra equations to model...Ch. 9.R - Prob. 1TFQCh. 9.R - Prob. 2TFQCh. 9.R - Prob. 3TFQCh. 9.R - Determine whether the statement is true or false....Ch. 9.R - Prob. 5TFQCh. 9.R - Determine whether the statement is true or false....Ch. 9.R - Prob. 7TFQCh. 9.R - Prob. 1ECh. 9.R - a Sketch a direction field for the differential...Ch. 9.R - a A direction field for the differential equation...Ch. 9.R - Prob. 4ECh. 9.R - Prob. 5ECh. 9.R - Prob. 6ECh. 9.R - 58 Solve the differential equation. 2yey2y=2x+3xCh. 9.R - 58 Solve the differential equation. x2yy=2x3e1/xCh. 9.R - 911 Solve the initial-value problem....Ch. 9.R - 911 Solve the initial-value problem....Ch. 9.R - Prob. 11ECh. 9.R - Prob. 12ECh. 9.R - 1314 Find the orthogonal trajectories of the...Ch. 9.R - Prob. 14ECh. 9.R - Prob. 15ECh. 9.R - a The population of the world was 6.1 billion in...Ch. 9.R - Prob. 17ECh. 9.R - Prob. 18ECh. 9.R - One model for the spread of an epidemic is that...Ch. 9.R - Prob. 20ECh. 9.R - Prob. 21ECh. 9.R - Populations of birds and insects are modeled by...Ch. 9.R - Prob. 23ECh. 9.R - Prob. 24ECh. 9.P - Find all functions f such that f is continuous and...Ch. 9.P - Prob. 2PCh. 9.P - Prob. 3PCh. 9.P - Find all functions f that satisfy the equation...Ch. 9.P - Prob. 5PCh. 9.P - A subtangent is a portion of the x-axis that lies...Ch. 9.P - A peach pie is taken out of the oven at 5:00 PM....Ch. 9.P - Snow began to fall during the morning of February...Ch. 9.P - A dog sees a rabbit running in a straight line...Ch. 9.P - a Suppose that the dog in Problem 9 runs twice as...Ch. 9.P - A planning engineer for a new alum plant must...Ch. 9.P - Prob. 12PCh. 9.P - Prob. 13PCh. 9.P - Prob. 14PCh. 9.P - Prob. 15PCh. 9.P - a An outfielder fields a baseball 280 ft away from...
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