4. Find the unit tangent, the principal normal, the curvature and wite an equation in x, y, z for the osculating plane at the point on the curve at t=0 and find the length from t=0 to t=ln3. (15%)

(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.)

4. Find the unit tangent, the principal normal, the curvature and wite an equation in x, y, z for the osculating plane at the point on the curve at t=0 and find the length from t=0 to t=ln3. (15%)

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