(b) (25 points) Suppose a vector field (x, y, z) = is defined over the surface σ of H. Let denote the outward unit normal vector of σ. Evaluate the integral ∫∫σdS.

(13) A logistic population model with relative growth rate 0.1 per year and carrying capacity 50 thousand can be expressed by the differential equation =0.1P(1 - ), with P in thousands and t in years. Given that the initial population is 9 thousand. Find the population size after 20 years. (If you memorized the formula, then you need to derive it for this problem.)

題組內容

(b) (25 points) Suppose a vector field (x, y, z) = is defined over the surface σ of H. Let denote the outward unit normal vector of σ. Evaluate the integral ∫∫_σdS.

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