Suppose you are studying bacteria in biology class the table shows the number of bacteria after n doubling periods
n(periods)[0 1 2 3 4 5]
billions of bacteria [3 6 12 24 48 96]
your teacher asks you to predict the number of bacteria after 8 doubling periods. what would your prediction be?
Period 6: 96*2
Period 7: 96*2²
Period 8: 96*2³
etc.
768
ewe
To predict the number of bacteria after 8 doubling periods, we can look for a pattern in the given data.
From the table, we can observe that each period is doubling the number of bacteria. In other words, the number of bacteria after each period is twice the number from the previous period.
We see that the number of bacteria after 0 doubling periods (n=0) is 3 billion. This serves as our starting point.
To find the number of bacteria after 8 doubling periods, we need to multiply the starting number (3 billion) by 2 eight times.
Using this pattern, we can calculate the prediction:
Number of bacteria after 8 doubling periods = 3 billion * (2^8)
= 3 billion * 256
= 768 billion
Therefore, the prediction for the number of bacteria after 8 doubling periods is 768 billion.