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.