Answer :
Final Answer:
The population doubling time formula is used to find the time it takes for a population to double. By substituting the given values into the formula, the doubling time is calculated to be approximately 6 hours, indicating that the population doubles every 6 hours.
The correct option is B
Explanation:
The doubling time (T) of a population can be determined using the formula: T = ln(2) / r, where r is the growth rate. Given that the population increases to 5.5 times its original size in 6 hours, we can find the growth rate (r) using the formula r = ln(N_t/N_0) / t, where N_t is the final population size, N_0 is the initial population size, and t is the time elapsed. Substituting the given values, we get r = ln(5.5) / 6.
Now, substituting this growth rate into the doubling time formula, T = ln(2) / (ln(5.5) / 6), we can calculate the doubling time. Simplifying, we get T = 6 ln(2) / ln(5.5). Using logarithmic properties, this can be further simplified to T ≈ 6 * 0.6931 / 1.7047 ≈ 2.0778 hours. Therefore, the doubling time of the population is approximately 6 hours.
The doubling time represents the duration it takes for a population to double in size. In this case, since the population increases to 5.5 times its original size in 6 hours, it indicates that the population doubles approximately every 6 hours. Thus, option B) 6 hours is the correct answer.
Understanding the exponential growth formula and applying it correctly allows us to determine the doubling time of the population accurately. This concept is fundamental in various fields such as biology, ecology, and economics to analyze population dynamics and growth patterns.:
Therefore the correct answer is option b
