Dr. Silas studies a culture of bacteria under a microscope. The function 1 ( ) 1200 1.8 ( ) t b t = represents the
number of bacteria t hours after Dr. Silas begins her study.
(a) What does the value 1200 represent in this situation?
(b) What does the value 1.8 represent in this situation?
(c) The number of bacteria in a second study is modeled by the function 2 ( ) 1000 1.8 ( )
t b t = .
What does the value of 1000 represent in this situation?
What does the difference of 1200 and 1000 mean between the two studies?

what is

step-by-step explanation:

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