Homework problems due on Thursday, Sept. 7

Exercise 1.1: Show that the solution of x’=re^-atx, x(0)=1 is the same as the solution of x’ = rx – ax ln x with x(0)= 1.

Exercise 1.2: True or false? Show your work in detail. A single cell of the bacterium E. coli would, under ideal
circumstances, divide every twenty minutes. … it can be shown that in a single day, one cell of E. coli could produce a
super-colony equal in size and weight to the entire planet earth.

Exercise 1.3: Problem 5, page 152.

Exercise 1.4: If this were a harvested population, where would you like to maintain the population size in order to manage
for Maximum Sustained Yield (MSY)? (Hint: Assume that the population is harvested at the rate of C/unit of time, then the
population grows according to dN/dt= rN(1-N/K)-C.)

Exercise 1.5: Problem 2(a, c), page 29

Exercise 1.6: Problem 3, page 29

Exercise 1.7: Problem 9, page 31. Use Matlab to graph the solutions with n=20.

Exercise 1.8: Problem 15, page 33.

Exercise 1.9: Problem 16, page 33.

Exercise 1.10: Problem 19, page 34.

Exercise 1.11: Problem 20, page 35.