At the beginning of an observational study, a culture contains 6,000 bacteria. After three hours, there are 9,500 bacteria. If the bacteria grow exponentially, Janice claims that there will be over 200,000 bacteria 20 hours
after their population reached 9,500. Is Janice correct? Justify your answer.
6004 entro

y=mx+

49%

step-by-step explanation:

when you realize that you dont know just realize i just took a test and im so smart

8+10

step-by-step explanation:

you multiply 4 by 2 and 5 by 2

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