4. 求線積分, 其中 C 是單位圓 x²+y²=1 在第一象限部份從(1,0) 到(0,1)的方向。(10分)

(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.)