Birth and death rates of animal populations typically are not constant; instead, they vary periodically with the passage of seasons. Find P(t) if the population P satisfies the differential equation
dP
dt

=(k+bcos2πt)P
where t is in years and k and b are positive constants. Thus the growth-rate function r(t)=k+bcos2πt varies periodically about its mean value k. Construct a graph that contrasts the growth of this population with one that has the same initial value P0 but satisfies the natural growth equation P0=kP (same constant k). How would the two populations compare after the passage of many years?

Come up with a new linear function that has a slope that falls in the range 10 m − < < . choose two different initial values. for this new linear function, what happens to the function’s values after many iterations? are the function’s values getting close to a particular number in each case?

Which number line represents the solution set for the inequality -1/2x> 24?

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.