A certain type of bacteria, given a favorable growth medium, doubles in population every 4 hours. Given that there were approximately 100 bacteria to start with, how many bacteria will there be in a day and a half?

To calculate the bacterial population after a day and a half with an initial count of 100 and a doubling time of 4 hours, we find 9 doubling periods in 36 hours. Using the exponential growth formula N = N0 * 2^n, we calculate the final population to be 51,200 bacteria.

Explanation:

The question involves an understanding of exponential growth, specifically concerning a population of bacteria. Given that the bacteria double in population every 4 hours, we first need to determine the number of doubling periods in a day and a half, which is equal to 36 hours. Since there are 4 hours in each doubling period, we divide 36 by 4 to get 9 doubling periods.

To find out the total number of bacteria after 36 hours, we use the formula for exponential growth:

N = N0 * 2^n

where N is the final population size, N0 is the initial population size, and n is the number of doubling periods.

Substituting the given values:

N = 100 * 2^9

N = 100 * 512

N = 51,200

Therefore, after a day and a half, there will approximately be 51,200 bacteria.

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