need these questions answered my homework is completed the completed graphs are attached All I need is questions answered.

Running Head: ASSIGNMENT 1: LASA 2: BACTERIAL GROWTH 1.

ASSIGNMENT 1: LASA 2: BACTERIAL GROWTH 2 .

ASSIGNMENT 1: LASA 2: BACTERIAL GROWTH 3.

Assignment.

Bacterial Sample	Hour 1	Hour 2	Hour 3	Hour 4	Hour 5	Hour 6	Hour 7
1	16	64	256	1024	4096	16,384	65,536
2	97	291	873	2619	7857	23,571	70,713
3	112	784	5488	38,416	268,912	1,882,384	13,176,688
4	7	63	567	5103	45,927	413,343	3,720,087
5	143	286	572	1144	2288	4576	9152

 

 

 

 

 

 

 

Solutions:

As I Determine the rate at which the culture grows in a hour. This rate will be the factor r by

which the number of bacterial cultures has increased since the last recorded observation.

Bacteria sample	A1(1st term)	A2(2nd term)	rn= an/an-1 i.e. (a2/a1)	R(common ratio)
1	16	64	64/16	4
2	97	291	291/97	3
3	112	784	784/112	7
4	7	63	63/7	9
5	143	286	286/143	2

 

As I take the time to write the formula that represents the growth of this bacteria based upon

my observations, I have found that my formula will be based upon the basic format for a

geometric sequence:

Bacteria sample 1:

An=a1rn-1

a1 =16

r=4

An =16(4n-1)

 

 

Bacteria sample 2:

An=a1rn-1

a1 =97

r=3

An =97(3 n-1)

Bacteria sample 3:

An=a1rn-1

a1 =112

r=7

An =112(7n-1)

Bacteria sample 4:

An=a1rn-1

a1 =7

r=9

An =7(9n-1)

 

 

Bacteria sample 5:

An=a1rn-1

a1 =143

r=2

An =143(2n-1)

Using the formula you’ve developed, determine the number of cultures you would expect to see

in the Petri dish on the 8th, 10th, and 12th hour of your observations.

Sample	1	2	3	4	5
1st term	16	97	112	7	143
ratio	4	3	7	9	2
Nth term (An=a1rn-1)
8th	16(48-1) =16(47) =262,144	97(38-1) =97(37) =212,139	112(78-1) =112(77) =92,236,816	7(98-1) =7(97) =33,480,783	143(28-1) =143(27) =18,304
10th	16(410-1) =16(49) =4,194,304	97(310-1) =97(39) =1,909,251	112(710-1) =112(79) =4,519,603,984	7(910-1) =7(99) =2,711,943,423	143(28-1) =143(27) =18,304
12th	16(412-1) =16(411) =67,108,864	97(312-1) =97(311) =17,183,259	112(712-1) =112(711) =2.215*1011	7(912-1) =7(911) =2.1967*1011	143(212-1) =143(211) =292,864

 

 

As I Compute the total number of bacterial cultures observed after 24 hours of growth assuming

that the growth follows a geometric series. My sample will look as follows.

Sample	1	2	3	4	5
1st term	16	97	112	7	143
Ratio	4	3	7	9	2
Nth term (An=a1rn-1)
24th	16(424-1) =16(423) =1.126*1015	97(324-1) =97(323) =9.132*1012	112(724-1) =112(723) =3.065*1021	7(924-1) =7(923) =6.204*1022	143(224-1) =143(223) =1.2*109