Aaliyah has a secret hobby – she is a rabid stamp collector. In fact, she has a terrific collection, but it would take a lot to have a complete collection. In looking through one of her philately magazines, she finds a table that gives the cumulative number of stamps S released by the United States Post Office in the years from 1889 to 1989, where t represents the number of years since 1889. t

0

10

20

30

40

50

60

70

80

90

100

S

218

293

374

541

681

858

986

1138

1138

1794

2438

3. Does the data show an increase that changes by a constant amount or by a constant rate?

4. Find a good model for the data. What is the function you wrote?

5. Aaliyah is missing the data for the year 1999. What is a good estimate for the number of stamps released through that year?

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.