Question

a culture of bacteria obeys the law of uninhibited growth. if 140,000 bacteria are present initially and there are 609,000 after 6 hours, how long will it take for the population to reach one million?

Answer 1

To calculate the time it takes for the population of bacteria to reach one million, we can use the formula for exponential growth: N = N0 * e^(rt). Given the initial and final populations, we can find the growth rate and then calculate the time.

Step-by-step explanation:

To calculate the time it takes for the population of bacteria to reach one million, we can use the formula for exponential growth: N = N0 * e^(rt), where N is the final population, N0 is the initial population, e is the base of the natural logarithm (approximately 2.71828), r is the growth rate, and t is the time elapsed.

Given that there are 140,000 bacteria initially and 609,000 bacteria after 6 hours, we can use these values to calculate the growth rate: 609,000 = 140,000 * e^(6r). Solving for r, we find r ≈ 0.1274.

Now, we can use the growth rate to find the time it takes for the population to reach one million: 1,000,000 = 140,000 * e^(0.1274t). Solving for t, we find t ≈ 16.88 hours.