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.

Question

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 &quot;y = ... .&quot;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.

Monica Dennis · Accepted Answer

The bacteria E get double every 10 minutes. soa.) if there is a single bacteria soafter 10 minutes number of bacterias will be double (2 times) of now = 2bacteriasafter 20 minutes number of bacterias will be double of number of bacteria after 10 minutes = 2*2 = 4bacteriasafter 30 minutes number of bacterias = 4*2 = 8bacteriasafter 40 minutes number of bacterias = 8*2 = 16bacteriasafter 50 minutes number of bacterias = 16*2 = 32bacteriasb.) to calculate the number of bacteria in the food after any 10 minutes1- 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 periodso we can write it &quot; y=2x &quot;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 = 1,073,741,824after 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

Bernard Boyer · Accepted Answer

c.) Time at which bacterias are calculated   Number of bacteriasat starting 1after 10 minutes 2after 20 minutes 4after 30 minutes 8after 40 minutes 16after 50 minutes 32after 60 minutes 64after 70 minutes 128after 80 minutes 256after 90 minutes 512after 100 minutes 1024after 110 minutes 2048after 120 minutes(2 hours) 4096the pattern of change from each time period to next is that they are getting doubled from previous time period.

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