11 The table below shows the amount of a decaying radioactive substance that remained for selected
years after 1990.
0
2
5
9
14
17
19
Years After 1990 (X)
Amount (9)
750
451
219
84
25
12
8
Write an exponential regression equation for this
set of data, rounding all values to the nearest
x thousandth. Using this equation, determine the
amount of the substance that remained in 2002, to
the nearest integer.

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.