Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 1.5, Problem 5PS
To determine
To find if the functions
are inverses of each other
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The spread of an infectious disease is often modeled using the following autonomous differential equation:
dI
-
- BI(N − I) − MI,
dt
where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of
transmission, and μ is the rate at which people recover from infection.
Close
a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria.
b) (5 points) For the equilbria in part a), determine whether each is stable or unstable.
c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the
dt
function by hand.) Identify the equilibria as stable or unstable in the graph.
d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.
Find the indefinite integral.
Check
Answer:
7x
4 + 1x
dx
show sketch
Chapter 1 Solutions
Calculus
Ch. 1.1 - Prob. 1PSCh. 1.1 - Prob. 2PSCh. 1.1 - Prob. 3PSCh. 1.1 - Prob. 4PSCh. 1.1 - Prob. 5PSCh. 1.1 - Prob. 6PSCh. 1.1 - Prob. 7PSCh. 1.1 - Prob. 8PSCh. 1.1 - Prob. 9PSCh. 1.1 - Prob. 10PS
Ch. 1.1 - Prob. 11PSCh. 1.1 - Prob. 12PSCh. 1.1 - Prob. 13PSCh. 1.1 - Prob. 14PSCh. 1.1 - Prob. 15PSCh. 1.1 - Prob. 16PSCh. 1.1 - Prob. 17PSCh. 1.1 - Prob. 18PSCh. 1.1 - Prob. 19PSCh. 1.1 - Prob. 20PSCh. 1.1 - Prob. 21PSCh. 1.1 - Prob. 22PSCh. 1.1 - Prob. 23PSCh. 1.1 - Prob. 24PSCh. 1.1 - Prob. 25PSCh. 1.1 - Prob. 26PSCh. 1.1 - Prob. 27PSCh. 1.1 - Prob. 28PSCh. 1.1 - Prob. 29PSCh. 1.1 - Prob. 30PSCh. 1.1 - Prob. 31PSCh. 1.1 - Prob. 32PSCh. 1.1 - Prob. 33PSCh. 1.1 - Prob. 34PSCh. 1.1 - Prob. 35PSCh. 1.1 - Prob. 36PSCh. 1.1 - Prob. 37PSCh. 1.1 - Prob. 38PSCh. 1.1 - Prob. 39PSCh. 1.1 - Prob. 40PSCh. 1.1 - Prob. 41PSCh. 1.1 - Prob. 42PSCh. 1.1 - Prob. 43PSCh. 1.1 - Prob. 44PSCh. 1.1 - Prob. 45PSCh. 1.1 - Prob. 46PSCh. 1.1 - Prob. 47PSCh. 1.1 - Prob. 48PSCh. 1.1 - Prob. 49PSCh. 1.1 - Prob. 50PSCh. 1.1 - Prob. 51PSCh. 1.1 - Prob. 52PSCh. 1.1 - Prob. 53PSCh. 1.1 - Prob. 54PSCh. 1.1 - Prob. 55PSCh. 1.1 - Prob. 56PSCh. 1.1 - Prob. 58PSCh. 1.1 - Prob. 59PSCh. 1.1 - Prob. 60PSCh. 1.2 - Prob. 1PSCh. 1.2 - Prob. 2PSCh. 1.2 - Prob. 3PSCh. 1.2 - Prob. 4PSCh. 1.2 - Prob. 5PSCh. 1.2 - Prob. 6PSCh. 1.2 - Prob. 7PSCh. 1.2 - Prob. 8PSCh. 1.2 - Prob. 9PSCh. 1.2 - Prob. 10PSCh. 1.2 - Prob. 11PSCh. 1.2 - Prob. 12PSCh. 1.2 - Prob. 13PSCh. 1.2 - Prob. 14PSCh. 1.2 - Prob. 15PSCh. 1.2 - Prob. 16PSCh. 1.2 - Prob. 17PSCh. 1.2 - Prob. 18PSCh. 1.2 - Prob. 19PSCh. 1.2 - Prob. 20PSCh. 1.2 - Prob. 21PSCh. 1.2 - Prob. 22PSCh. 1.2 - Prob. 23PSCh. 1.2 - Prob. 24PSCh. 1.2 - Prob. 25PSCh. 1.2 - Prob. 26PSCh. 1.2 - Prob. 27PSCh. 1.2 - Prob. 28PSCh. 1.2 - Prob. 29PSCh. 1.2 - Prob. 30PSCh. 1.2 - Prob. 31PSCh. 1.2 - Prob. 32PSCh. 1.2 - Prob. 33PSCh. 1.2 - Prob. 34PSCh. 1.2 - Prob. 35PSCh. 1.2 - Prob. 36PSCh. 1.2 - Prob. 37PSCh. 1.2 - Prob. 38PSCh. 1.2 - Prob. 39PSCh. 1.2 - Prob. 40PSCh. 1.2 - Prob. 41PSCh. 1.2 - Prob. 42PSCh. 1.2 - Prob. 43PSCh. 1.2 - Prob. 44PSCh. 1.2 - Prob. 45PSCh. 1.2 - Prob. 46PSCh. 1.2 - Prob. 47PSCh. 1.2 - Prob. 48PSCh. 1.2 - Prob. 49PSCh. 1.2 - Prob. 50PSCh. 1.2 - Prob. 51PSCh. 1.2 - Prob. 52PSCh. 1.2 - Prob. 53PSCh. 1.2 - Prob. 54PSCh. 1.2 - Prob. 55PSCh. 1.2 - Prob. 56PSCh. 1.2 - Prob. 57PSCh. 1.2 - Prob. 58PSCh. 1.2 - Prob. 59PSCh. 1.2 - Prob. 60PSCh. 1.3 - Prob. 1PSCh. 1.3 - Prob. 2PSCh. 1.3 - Prob. 3PSCh. 1.3 - Prob. 4PSCh. 1.3 - Prob. 5PSCh. 1.3 - Prob. 6PSCh. 1.3 - Prob. 7PSCh. 1.3 - Prob. 8PSCh. 1.3 - Prob. 9PSCh. 1.3 - Prob. 10PSCh. 1.3 - Prob. 11PSCh. 1.3 - Prob. 12PSCh. 1.3 - Prob. 13PSCh. 1.3 - Prob. 14PSCh. 1.3 - Prob. 15PSCh. 1.3 - Prob. 16PSCh. 1.3 - Prob. 17PSCh. 1.3 - Prob. 18PSCh. 1.3 - Prob. 19PSCh. 1.3 - Prob. 20PSCh. 1.3 - Prob. 21PSCh. 1.3 - Prob. 22PSCh. 1.3 - Prob. 23PSCh. 1.3 - Prob. 24PSCh. 1.3 - Prob. 25PSCh. 1.3 - Prob. 26PSCh. 1.3 - Prob. 27PSCh. 1.3 - Prob. 28PSCh. 1.3 - Prob. 29PSCh. 1.3 - Prob. 30PSCh. 1.3 - Prob. 31PSCh. 1.3 - Prob. 32PSCh. 1.3 - Prob. 33PSCh. 1.3 - Prob. 34PSCh. 1.3 - Prob. 35PSCh. 1.3 - Prob. 36PSCh. 1.3 - Prob. 37PSCh. 1.3 - Prob. 38PSCh. 1.3 - Prob. 39PSCh. 1.3 - Prob. 40PSCh. 1.3 - Prob. 41PSCh. 1.3 - Prob. 42PSCh. 1.3 - Prob. 43PSCh. 1.3 - Prob. 44PSCh. 1.3 - Prob. 45PSCh. 1.3 - Prob. 46PSCh. 1.3 - Prob. 47PSCh. 1.3 - Prob. 48PSCh. 1.3 - Prob. 49PSCh. 1.3 - Prob. 50PSCh. 1.3 - Prob. 51PSCh. 1.3 - Prob. 52PSCh. 1.3 - Prob. 53PSCh. 1.3 - Prob. 54PSCh. 1.3 - Prob. 55PSCh. 1.3 - Prob. 56PSCh. 1.3 - Prob. 57PSCh. 1.3 - Prob. 58PSCh. 1.3 - Prob. 59PSCh. 1.3 - Prob. 60PSCh. 1.4 - Prob. 1PSCh. 1.4 - Prob. 2PSCh. 1.4 - Prob. 3PSCh. 1.4 - Prob. 4PSCh. 1.4 - Prob. 5PSCh. 1.4 - Prob. 6PSCh. 1.4 - Prob. 7PSCh. 1.4 - Prob. 8PSCh. 1.4 - Prob. 9PSCh. 1.4 - Prob. 10PSCh. 1.4 - Prob. 11PSCh. 1.4 - Prob. 12PSCh. 1.4 - Prob. 13PSCh. 1.4 - Prob. 14PSCh. 1.4 - Prob. 15PSCh. 1.4 - Prob. 16PSCh. 1.4 - Prob. 17PSCh. 1.4 - Prob. 18PSCh. 1.4 - Prob. 19PSCh. 1.4 - Prob. 20PSCh. 1.4 - Prob. 21PSCh. 1.4 - Prob. 22PSCh. 1.4 - Prob. 23PSCh. 1.4 - Prob. 24PSCh. 1.4 - Prob. 25PSCh. 1.4 - Prob. 26PSCh. 1.4 - Prob. 27PSCh. 1.4 - Prob. 28PSCh. 1.4 - Prob. 29PSCh. 1.4 - Prob. 30PSCh. 1.4 - Prob. 31PSCh. 1.4 - Prob. 32PSCh. 1.4 - Prob. 33PSCh. 1.4 - Prob. 34PSCh. 1.4 - Prob. 35PSCh. 1.4 - Prob. 36PSCh. 1.4 - Prob. 37PSCh. 1.4 - Prob. 38PSCh. 1.4 - Prob. 39PSCh. 1.4 - Prob. 40PSCh. 1.4 - Prob. 41PSCh. 1.4 - Prob. 42PSCh. 1.4 - Prob. 43PSCh. 1.4 - Prob. 44PSCh. 1.4 - Prob. 45PSCh. 1.4 - Prob. 46PSCh. 1.4 - Prob. 47PSCh. 1.4 - Prob. 48PSCh. 1.4 - Prob. 49PSCh. 1.4 - Prob. 50PSCh. 1.4 - Prob. 51PSCh. 1.4 - Prob. 52PSCh. 1.4 - Prob. 53PSCh. 1.4 - Prob. 54PSCh. 1.4 - Prob. 55PSCh. 1.4 - Prob. 56PSCh. 1.4 - Prob. 57PSCh. 1.4 - Prob. 58PSCh. 1.4 - Prob. 59PSCh. 1.4 - Prob. 60PSCh. 1.5 - Prob. 1PSCh. 1.5 - Prob. 2PSCh. 1.5 - Prob. 3PSCh. 1.5 - Prob. 4PSCh. 1.5 - Prob. 5PSCh. 1.5 - Prob. 6PSCh. 1.5 - Prob. 7PSCh. 1.5 - Prob. 8PSCh. 1.5 - Prob. 9PSCh. 1.5 - Prob. 10PSCh. 1.5 - Prob. 11PSCh. 1.5 - Prob. 12PSCh. 1.5 - Prob. 13PSCh. 1.5 - Prob. 14PSCh. 1.5 - Prob. 15PSCh. 1.5 - Prob. 16PSCh. 1.5 - Prob. 17PSCh. 1.5 - Prob. 18PSCh. 1.5 - Prob. 19PSCh. 1.5 - Prob. 20PSCh. 1.5 - Prob. 21PSCh. 1.5 - Prob. 22PSCh. 1.5 - Prob. 23PSCh. 1.5 - Prob. 24PSCh. 1.5 - Prob. 25PSCh. 1.5 - Prob. 26PSCh. 1.5 - Prob. 27PSCh. 1.5 - Prob. 28PSCh. 1.5 - Prob. 29PSCh. 1.5 - Prob. 30PSCh. 1.5 - Prob. 31PSCh. 1.5 - Prob. 32PSCh. 1.5 - Prob. 33PSCh. 1.5 - Prob. 34PSCh. 1.5 - Prob. 35PSCh. 1.5 - Prob. 36PSCh. 1.5 - Prob. 37PSCh. 1.5 - Prob. 38PSCh. 1.5 - Prob. 39PSCh. 1.5 - Prob. 40PSCh. 1.5 - Prob. 41PSCh. 1.5 - Prob. 42PSCh. 1.5 - Prob. 43PSCh. 1.5 - Prob. 44PSCh. 1.5 - Prob. 45PSCh. 1.5 - Prob. 46PSCh. 1.5 - Prob. 47PSCh. 1.5 - Prob. 48PSCh. 1.5 - Prob. 49PSCh. 1.5 - Prob. 50PSCh. 1.5 - Prob. 51PSCh. 1.5 - Prob. 52PSCh. 1.5 - Prob. 53PSCh. 1.5 - Prob. 54PSCh. 1.5 - Prob. 55PSCh. 1.5 - Prob. 56PSCh. 1.5 - Prob. 57PSCh. 1.5 - Prob. 58PSCh. 1.5 - Prob. 59PSCh. 1.5 - Prob. 60PSCh. 1 - Prob. 1PECh. 1 - Prob. 2PECh. 1 - Prob. 3PECh. 1 - Prob. 4PECh. 1 - Prob. 5PECh. 1 - Prob. 6PECh. 1 - Prob. 7PECh. 1 - Prob. 8PECh. 1 - Prob. 9PECh. 1 - Prob. 10PECh. 1 - Prob. 11PECh. 1 - Prob. 12PECh. 1 - Prob. 13PECh. 1 - Prob. 14PECh. 1 - Prob. 15PECh. 1 - Prob. 16PECh. 1 - Prob. 17PECh. 1 - Prob. 18PECh. 1 - Prob. 19PECh. 1 - Prob. 20PECh. 1 - Prob. 21PECh. 1 - Prob. 22PECh. 1 - Prob. 23PECh. 1 - Prob. 24PECh. 1 - Prob. 25PECh. 1 - Prob. 26PECh. 1 - Prob. 27PECh. 1 - Prob. 28PECh. 1 - Prob. 29PECh. 1 - Prob. 30PECh. 1 - Prob. 1SPCh. 1 - Prob. 2SPCh. 1 - Prob. 3SPCh. 1 - Prob. 4SPCh. 1 - Prob. 5SPCh. 1 - Prob. 6SPCh. 1 - Prob. 7SPCh. 1 - Prob. 8SPCh. 1 - Prob. 9SPCh. 1 - Prob. 10SPCh. 1 - Prob. 11SPCh. 1 - Prob. 12SPCh. 1 - Prob. 13SPCh. 1 - Prob. 14SPCh. 1 - Prob. 15SPCh. 1 - Prob. 16SPCh. 1 - Prob. 17SPCh. 1 - Prob. 18SPCh. 1 - Prob. 19SPCh. 1 - Prob. 20SPCh. 1 - Prob. 21SPCh. 1 - Prob. 22SPCh. 1 - Prob. 23SPCh. 1 - Prob. 24SPCh. 1 - Prob. 25SPCh. 1 - Prob. 26SPCh. 1 - Prob. 27SPCh. 1 - Prob. 28SPCh. 1 - Prob. 29SPCh. 1 - Prob. 30SPCh. 1 - Prob. 31SPCh. 1 - Prob. 32SPCh. 1 - Prob. 33SPCh. 1 - Prob. 34SPCh. 1 - Prob. 35SPCh. 1 - Prob. 36SPCh. 1 - Prob. 37SPCh. 1 - Prob. 38SPCh. 1 - Prob. 39SPCh. 1 - Prob. 40SPCh. 1 - Prob. 41SPCh. 1 - Prob. 42SPCh. 1 - Prob. 43SPCh. 1 - Prob. 44SPCh. 1 - Prob. 45SPCh. 1 - Prob. 46SPCh. 1 - Prob. 47SPCh. 1 - Prob. 48SPCh. 1 - Prob. 49SPCh. 1 - Prob. 50SPCh. 1 - Prob. 51SPCh. 1 - Prob. 52SPCh. 1 - Prob. 53SPCh. 1 - Prob. 54SPCh. 1 - Prob. 55SPCh. 1 - Prob. 56SPCh. 1 - Prob. 57SPCh. 1 - Prob. 58SPCh. 1 - Prob. 59SPCh. 1 - Prob. 60SPCh. 1 - Prob. 61SPCh. 1 - Prob. 62SPCh. 1 - Prob. 63SPCh. 1 - Prob. 64SPCh. 1 - Prob. 65SPCh. 1 - Prob. 66SPCh. 1 - Prob. 67SPCh. 1 - Prob. 68SPCh. 1 - Prob. 69SPCh. 1 - Prob. 70SPCh. 1 - Prob. 71SPCh. 1 - Prob. 72SPCh. 1 - Prob. 73SPCh. 1 - Prob. 74SPCh. 1 - Prob. 75SPCh. 1 - Prob. 76SPCh. 1 - Prob. 77SPCh. 1 - Prob. 78SPCh. 1 - Prob. 79SPCh. 1 - Prob. 80SPCh. 1 - Prob. 81SPCh. 1 - Prob. 82SPCh. 1 - Prob. 83SPCh. 1 - Prob. 84SPCh. 1 - Prob. 85SPCh. 1 - Prob. 86SPCh. 1 - Prob. 93SPCh. 1 - Prob. 95SPCh. 1 - Prob. 96SPCh. 1 - Prob. 97SPCh. 1 - Prob. 98SPCh. 1 - Prob. 99SP
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