MAT-470 Exam 2
For each question, make sure you justify your solutions.
???
??
1. The logistic differential equation is ??? = ???? (1 ? ??) where K is the carrying capacity, r
is the growth rate, and P is the population at time t. Suppose a population of fruit flies is
observed to be 200 at t = 0. After one day, the population had increased by 4%. If the
carrying capacity in this area is 1500 fruit flies,
(a) Write the logistic differential equation and initial condition for this model.
(b) Solve the initial value problem for P(t).
(c) Use the solution to predict the population after 3 days.
2. Solve ???? ? + (?? ? 2)?? = 3?? 3 ? ??? , y(1) = 0
3. Use Euler’s method to calculate the first three approximations to the given initial value
problem for the specified increment size. Round your results to four decimal places.
?? ? = 3???? + ??, y(0) = 2, ???? = 0.2

Purchase answer to see full
attachment