After the closing of the mill, the town of Sawyerville experienced a decline in its population.
The relationship between the elapsed time, ttt, in years, since the closing of the mill, and the town's population, P(t)P(t)P, left parenthesis, t, right parenthesis, is modeled by the following function.
P(t)=12,000⋅2−t15
In how many years will Sawyerville's population be 9000?
Round your answer, if necessary, to the nearest hundredth.

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?