Final answer:
To calculate how long it will take for the population of bacteria to reach 200,000, we need to determine the number of times the population doubles. Using the formula final population = initial population * (2 ^ n), where n is the number of times the population doubles, we can calculate that it will take approximately 11 doublings, or 33 hours, for the population of bacteria to reach 200,000.
Step-by-step explanation:
To calculate how long it will take for the population of bacteria to reach 200,000, we need to determine how many times the population doubles. Each time the population doubles, it multiplies by 2. So, we can use the formula: final population = initial population * (2 ^ n), where n is the number of times the population doubles.
In this case, the initial population is 100 and the final population is 200,000. We can rewrite the formula as: 200,000 = 100 * (2 ^ n). To solve for n, we need to isolate the exponent by dividing both sides of the equation by 100: (2 ^ n) = 2000. Next, we take the logarithm base 2 of both sides: n = log2(2000) = 10.96. Therefore, it will take approximately 11 doublings, or 11 * 3 = 33 hours, for the population of bacteria to reach 200,000.