Question

a bacteria culture begins with 11 bacteria that triple in amount at the end of every hour. how many bacteria are grown during the 7th hour?
1,331
8,019
9,317
24,057

Explanation:

Step1: Find bacteria amount at 6th hour

The formula for the amount of bacteria after $n$ hours is $a_n=a_0\times3^n$, where $a_0 = 11$. For $n = 6$, $a_6=11\times3^6=11\times729 = 8019$.

Step2: Find bacteria amount at 7th hour

For $n = 7$, $a_7=11\times3^7=11\times2187 = 24057$.

Step3: Calculate growth in 7th hour

Subtract the amount at 6th hour from the amount at 7th hour. Growth = $a_7 - a_6=24057-8019 = 16038$. But there seems to be a misunderstanding in the problem - if we assume it wants the amount at the end of the 7th hour instead of the growth during the 7th hour, then the amount of bacteria at the end of the 7th hour is $a_7=11\times3^7 = 24057$.

Answer:

24057