A type of bacteria reproduces by splitting in two every thirty minutes. How many bacteria will there be after 4 hours if there are 2 bacteria to begin with?

To determine the number of bacteria after 4 hours, we need to calculate the number of times the bacteria can multiply in that duration.

Given that the bacteria split in two every 30 minutes, we can calculate the number of splitting cycles in 4 hours:

4 hours = 4 x 60 minutes/hour = 240 minutes.

Since each splitting cycle takes 30 minutes, we divide the total minutes (240) by the splitting cycle time (30) to determine the number of cycles:

240 minutes / 30 minutes per cycle = 8 cycles.

In each cycle, the number of bacteria doubles. Since we start with 2 bacteria, after each cycle, the number of bacteria is 2 times the previous count.

To find the final number of bacteria after 8 cycles, we can use the exponential growth formula:

Final count = Initial count × (2 ^ Number of cycles)

Plugging in the values, we get:

Final count = 2 bacteria × (2 ^ 8 cycles)

To calculate 2 raised to the power of 8, we multiply 2 by itself 8 times:

2 ^ 8 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256.

Now, we can substitute this value into the formula:

Final count = 2 bacteria × 256

Final count = 512 bacteria.

Therefore, after 4 hours, starting with 2 bacteria, there will be 512 bacteria.