MATH 102 Lecture Notes - Lecture 16: Logistic Function, Pythagorean Theorem
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Example 1: logistic growth rate: small populations % large populations grow slowly, equation: # K: n: density of the population, g: growth rate, r, k - constants, for which values of n is g(n) = 0, rn = 0 or # ) = 0: g(n) < 0 means the population is declining, k can be interpreted as the carrying capacity of the function, therefore, when population density n reaches k/2, the population density achieves maximum growth rate. Example 2: cell surface area: some cells look like cylinder-shaped, they have a xed volume, goal: to minimize surface area. Step 1: find the equation of the volume and surface area of cylinder. Step 2: since there are two unknown variable, substitute one out using the volume formula to nd. Step 3: plug l in terms of r into the surface area formula. R 2 ) + 2 r 2 2(
