There are many important classes of species whose birthrate is not proportional to the population size N(t). Suppose, for example, that each member of the population requires a partner for reproduction and that each member relies on chance encounters to meet a mate. If the expected number of encounters is proportional to the product of the numbers of males and females, and if these are equally distributed in the population, then the number of encounters, and hence the birthrate, is proportional to N(t)2. The death rate is still proportional to N(t). Consequently, the population size N(t) satisfies the differential equation:
dN/dt = bN² - aN,
where a and b are positive constants.
(a) Solve for N(t) given N(0).
(b) Find the long term behavior by taking t→[infinity] in your solution in (a). Do this for the case N(0) < a/b.

Compare the following pair of numbers a and b in three ways. a. find the ratio of a to b. b. find the ratio of b to a. c. complete the sentence: a is percent of b. a=120 and b=340 a. the ratio of a to b is . b. the ratio of b to a is . c. a is nothing percent of b.

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i. e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)

What are two numbers that add up to -9 and multiply to -10 best answer gets branliest and 100 extra points