Write a rule for the table below
Hours Number of Bacteria
1 32
2 256
3 2048
4 16384
5 131072
6 1048567
well 1048567/131072 = 7.999931 close to 8
try the first one
256/32 = 8
hmm, next one
2048 / 256 = 8
hmmmm
suspect geometric sequence with a = 32 and r = 8
but try next to make sure
16384 / 2048 = 8 sure enough
so
term n = 32 * 8^(n-1)
To find the number of bacteria as a function of hours, we notice that the number of bacteria is increasing exponentially. Each time the hours increase by 1, the number of bacteria is multiplied by 8. Therefore, the rule for the table is:
Number of Bacteria = 32 * (8)^(Hours - 1)
To write a rule for the given table, we need to find the pattern or relationship between the hours and the number of bacteria.
Looking at the numbers in the "Number of Bacteria" column, we can notice that each number is obtained by multiplying the previous number by 8.
Starting from the first row, we can see that:
32 * 8 = 256
256 * 8 = 2048
2048 * 8 = 16384
16384 * 8 = 131072
131072 * 8 = 1048576
So, the pattern is that each number in the "Number of Bacteria" column is obtained by multiplying the previous number by 8.
Hence, the rule for the table is:
Number of Bacteria = (Previous Number of Bacteria) * 8