Question

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The doubling time of a population of fles is 4 hours. By what factor does the population increase in 25 hours? By what factor does the population increase in 1 week?
By what factor does the population increase in 25 hours?
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(Type exponential notation with positive exponents. Use integers or decimals for any numbers in the expression.)
By what factor does the population increase in 1 week?

Answer 1

The doubling time of a flea population is 4 hours. The population increases by a factor of 2^6 in 25 hours and by a factor of 2^42 in 1 week.

Step-by-step explanation:

The population of a species is said to double when it becomes twice as large as its original size. The doubling time is the amount of time it takes for a population to double in size. In this case, the doubling time of the flea population is given as 4 hours.

To find the factor by which the population increases in 25 hours, we can calculate the number of doubling cycles that occur in that time period. Since each doubling cycle is 4 hours, 25 hours would have 6 full doubling cycles (25 / 4 = 6.25). So, the population would increase by a factor of 2 raised to the power of 6, which can be written as 2^6.

To find the factor by which the population increases in 1 week (168 hours), we divide the total time by the doubling time. 168 / 4 = 42. So, the population would increase by a factor of 2 raised to the power of 42, which can be written as 2^42.

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