2. Use Euler's method to approximate the given value ofy(t) with the time step h indicated. Make sure to include each point that you find in your process. (10 pts) y(3.3) E9; = t2 y y(3) = 1 h = 0.1 3. Suppose that a population develops according to the logistic equation 2: = 0.5P 0.0025P2 where t is measured in weeks. (10 points) a) What is the carrying capacity? b) For what interval is the population increasing? (3) For what interval is the population decreasing? d) Find the general solution for P(t). e) Find the particular solution for P(0) = 500. 4. The population P(t) of mosquito larvae growing in a tree hole increases according to the logistic equation with growth constant k = 0.3 day1 and carrying capacity A = 500. (10 points) a) Find a formula for the larvae population PCt), assuming an initial population P0 : 50 larvae. b) After how many days will the larvae population reach 200