In Problem use a graphing calculator to graph the given examples of the various cases in Table 1.

Exponential decay:

p = 100e^-0.05x
0 ≤ x ≤ 30
0 ≤ p ≤ 100

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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