8.求曲線 (t) = 3cos(t)+ 3sin(t) + 4t= (3cos(t), 3sin(t), 4t) 在 t 時的切線單位向量與法線單位向量,並求其曲率。(13 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.)