The bacteria E coli often causes illness among people who ea

The bacteria E. coli often causes illness among people who eat the infected food. Suppose a single E. coli bacterium in a batch of ground beef begins doubling every 10 minutes.

a. How many bacteria will there be after 10, 20, 30, 40, and 50 minutes have elapsed? Assume no bacteria die.

b. Write two rules that can be used to calculate the number of bacteria in the food after any number of 10-minute periods-one using NOW and NEXT, and aother begin \"y = ... .\"

c. Use your rules to make a table showing the number of E. coli bacteria in the batch of ground beef at the end of each 10-minute period over 2 hours. Then describe the pattern of change in the number of bacteria from each time period to the next.

d. Find the predicted number of bacteria after 4, 5, and 6 hours.

Solution

The bacteria E get double every 10 minutes. so

a.) if there is a single bacteria so

after 10 minutes number of bacterias will be double (2 times) of now = 2bacterias

after 20 minutes number of bacterias will be double of number of bacteria after 10 minutes = 2*2 = 4bacterias

after 30 minutes number of bacterias = 4*2 = 8bacterias

after 40 minutes number of bacterias = 8*2 = 16bacterias

after 50 minutes number of bacterias = 16*2 = 32bacterias

b.) to calculate the number of bacteria in the food after any 10 minutes

1- if NOW the number of bacteria is 1 NEXT time(after 10 minutes) it will be 2 (double of NOW / or 2 times of NOW).

2- number of bacteria y after x number of 10-minutes time period

so we can write it \" y=2^x \"

c.)

Time at which bacterias are calculated

Number of bacterias

at starting

1

after 10 minutes

2

after 20 minutes

4

after 30 minutes

8

after 40 minutes

16

after 50 minutes

32

after 60 minutes

64

after 70 minutes

128

after 80 minutes

256

after 90 minutes

512

after 100 minutes

1024

after 110 minutes

2048

after 120 minutes(2 hours)

4096

the pattern of change from each time period to next is that they are getting doubled from previous time period.

d.) after 4 hours- in 4 hours there will 24 time periods of 10-minute.

so number of bacteria after 4 hours= 2²⁴ = 16,777,216   

after 5 hours- in 5 hours there will 30 time periods of 10-minute.

so number of bacteria after 4 hours= 2³⁰ = 1,073,741,824

after 6 hours- in 6 hours there will 36 time periods of 10-minute.

so number of bacteria after 6 hours= 2³⁶ = 68,719,476,736

Time at which bacterias are calculated	Number of bacterias
at starting	1
after 10 minutes	2
after 20 minutes	4
after 30 minutes	8
after 40 minutes	16
after 50 minutes	32
after 60 minutes	64
after 70 minutes	128
after 80 minutes	256
after 90 minutes	512
after 100 minutes	1024
after 110 minutes	2048
after 120 minutes(2 hours)	4096