A certain bacterium divides into 2 bacteria every 20 minutes. If there are four bacteria in the culture now, how many will there be in 4 hours, assuming that no bacteria die?
population doubles every 20 minutes, or 3 times per hour. So, every hour, the population grows by a factor of 8.
So, since we are starting at p(0) = 4,
p(h) = 4*8^h
gives the population after h hours.
p(4) = 4*8^4 = 4*4096 = 16384
X=N.2n
X=N.2(48)
X=N(24)
X=24
To determine the number of bacteria in 4 hours, we need to calculate the number of cycles the bacterium undergoes within that time.
Given that the bacterium divides into 2 every 20 minutes, we can calculate the number of cycles by dividing the total time (4 hours) by the time it takes for a complete cycle (20 minutes).
4 hours is equal to 4 * 60 = 240 minutes.
Since each cycle takes 20 minutes, the number of cycles within 240 minutes is 240 / 20 = 12 cycles.
Starting with 4 bacteria, each cycle doubles the population. Therefore, the number of bacteria after 12 cycles will be 4 * 2^12.
Using exponentiation, we can calculate this as:
4 * 2^12 = 4 * 4096 = 16,384 bacteria.
Therefore, there will be 16,384 bacteria in the culture after 4 hours, assuming no bacteria die.