The table shows the approximate population of Virginia for 5 years. If the trend continues, which could be a reasonable prediction of the
population in 2012?
Year
2000
2004
2006
2007
2008
Population
(Millions)
7.08
7.48
7.64
7.71
7.77
A. 7.83 million people
B. 7.96 million people
C. 8.17 million people
D. 8.42 million people

she will most likely have 33  

step-by-step explanation:

i think is g(1)=-1.

hope that i can

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt