After a special medicine is introduced into a petri dish containing a bacterial culture, the number of bacteria remaining in the dish decreases rapidly. The population loses \dfrac 14 4 1 start fraction, 1, divided by, 4, end fraction of its size every 444444 seconds. The number of remaining bacteria can be modeled by a function, NNN, which depends on the amount of time, ttt (in seconds). Before the medicine was introduced, there were 11{,}88011,88011, comma, 880 bacteria in the Petri dish. Write a function that models the number of remaining bacteria ttt seconds since the medicine was introduced.

Can someone me with the property questions for 12 13 and 14 plz

8litres of paint can cover 129.6 m². how much paint is required to paint an area of 243m²?

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.