# 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 pblackicted number of bacteria after 4, 5, and 6 hours.

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 pblackicted number of bacteria after 4, 5, and 6 hours.
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Monica Dennis
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=2x "
d.) after 4 hours- in 4 hours there will 24 time periods of 10-minute.
so number of bacteria after 4 hours= 2^24 = 16,777,216
after 5 hours- in 5 hours there will 30 time periods of 10-minute.
so number of bacteria after 4 hours= 2^30 = 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= 2^36 = 68,719,476,736
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Bernard Boyer
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.