Bacterial populations can grow to enormous numbers in a matter of a few hours with the right conditions. If a bacterial colony doubles size every 15 minutes, how many bacteria will be present after 1 hour if the colony began with 4 bacteria?
4, 16, 32, 64, 128
4*2^n
n = 4 quarters of and hour
2^4 = 16
so
4*16 = 64
ah
4 8 16 32 64
Ooops!
Thanks, Damon. :-)
Thanks so much. Since my school has homework warnings, you saved me from a homework warning and from causing my grade to go down.
To calculate the number of bacteria after 1 hour, we need to determine the number of times the bacterial population doubles in that duration.
Given that the bacterial colony doubles in size every 15 minutes, we can calculate the number of doubling cycles in 1 hour:
Since there are 60 minutes in an hour and each doubling cycle takes 15 minutes, we can divide 60 by 15 to get the number of doubling cycles:
60 minutes ÷ 15 minutes = 4 doubling cycles
So, the bacterial population will double 4 times within 1 hour.
Starting with 4 bacteria, if the population doubles with each cycle, we can calculate the population after 1 hour using the formula:
Population after n cycles = Initial population * (2^n)
Therefore, the population after 4 doubling cycles is:
Population after 4 cycles = 4 bacteria * (2^4)
Calculating this, we find:
2^4 = 2 * 2 * 2 * 2 = 16
Population after 4 cycles = 4 bacteria * 16 = 64 bacteria
Hence, after 1 hour, the bacterial colony will have grown to a population of 64 bacteria.