A culture of bacteria has an initial population of 39000 bacteria and doubles every 9 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t

=P
0

⋅2
d
t


, where P_tP
t

is the population after t hours, P_0P
0

is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 2 hours, to the nearest whole number?

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?