Matilda has been studying exponential functions in her algebra class and has started to notice a pattern.

For some exponential functions, when she plugs in larger and larger numbers, she gets larger and larger numbers. For others, she gets smaller and smaller numbers. And for some, plugging in larger and larger numbers actually gets her closer and closer to one number.

Which of the following exponential functions get closer and closer to one value as you plug-in larger and larger values for x?

Select one:
A. f(x)=0.45(1.9)x
B. f(x)=−7(2)x
C. f(x)=(34)x+9
D. f(x)=(65)x−6

If x = ∛200, which of the following inequalities is true? * 2 < x < 4 3 < x < 5 6 < x < 6.5 4.5 < x < 5.5 5 < x < 6

Me. i can't figure out this question. give an explanation too. .

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.