Consider the differential equationdPdt= kP1 + c, wherek > 0andc ≥ 0.In Section 3.1 we saw that in the casec = 0the linear differential equationdP/dt = kPis a mathematical model of a population P(t) that exhibits unbounded growth over the infinite time interval[0, [infinity]),that is, P(t) → [infinity]ast → [infinity].See Example 1 in that section.(a) Suppose forc = 0.01that the nonlinear differential equationdPdt= kP1.01, k > 0,is a mathematical model for a population of small animals, where time t is measured in months. Solve the differential equation subject to the initial conditionP(0) = 10and the fact that the animal population has doubled in 6 months. (Round the coefficient of t to six decimal places.)P(t) =(b) The differential equation in part (a) is called a doomsday equation because the population P(t) exhibits unbounded growth over a finite time interval(0, T),that is, there is some time T such thatP(t) → [infinity]ast → T −.Fin

The random variable x represents the number of phone calls an author receives in a day, and it has a poisson distribution with a mean of 8.7 calls. what are the possible values of x

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?

An annual marathon covers a route that has a distance of approximately 26 miles. winning times for this marathon are all over 2 hours. the following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. earlier period 14 12 15 22 13 10 19 13 9 14 20 18 16 20 23 12 18 17 6 13 recent period 7 11 7 14 8 9 11 14 8 7 9 8 7 9 9 9 9 8 10 8 (a) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks. for more details, view how to split a stem.) minutes beyond 2 hours earlier period 0 1 2 (b) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks.) minutes beyond 2 hours recent period (c) compare the two distributions. how many times under 15 minutes are in each distribution