In Problem use a graphing calculator to graph the given examples of the various cases in Table
Question:
In Problem use a graphing calculator to graph the given examples of the various cases in Table 1.
Unlimited growth:
y = 1,000e0.08t
0 ≤ t ≤ 15
0 ≤ y ≤ 3,500
Transcribed Image Text:
Table 1 Exponential Growth Description Model Solution Graph Uses Unlimited growth: Rate of growth is proportional to the amount present Short-term population growth (people, bacteria, etc.) Growth of money at continuous compound interest Price-supply curves dy = ky dt y = cet y k, t >0 y(0) = c • Depletion of natural resources • Radioactive decay • Absorption of light in water • Price-demand curves • Atmospheric pressure (t is altitude) Exponential decay: Rate of growth is proportional to the amount present dy -ky y = ce t dt k, t >0 y(0) = c Sales fads (new phones, trending Limited growth: Rate of growth is proportional dy y = M(1 - e = k(M - y) dt fashion) M Depreciation of equipment • Company growth • Learning to the difference between k, t >0 the amount present and a fixed limit y(0) = 0 Logistic growth: Rate of growth is proportional to the amount present and Long-term population growth Epidemics • Sales of new products Spread of a rumor Company growth dy = ky(M - y) M y = dt 1 + ce kMI M to the difference between k, t >0 the amount present and a M fixed limit y(0) 1 + c
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College Mathematics For Business Economics, Life Sciences, And Social Sciences
ISBN: 978-0134674148
14th Edition
Authors: Raymond Barnett, Michael Ziegler, Karl Byleen, Christopher Stocker
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