Question

In a lab experiment, 50 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 16 hours. How long would it be, to the nearest tenth of an hour, until there are 170 bacteria present?

Answer 1

To determine the time it would take for 170 bacteria to be present, we can set up an equation and solve for the number of doubling times. It would take approximately 48 hours for there to be 170 bacteria present.

Step-by-step explanation:

To solve this problem, we need to determine how many times the population will double in order to reach 170 bacteria.

Since the population doubles every 16 hours, we can set up an equation to solve for the number of doubling times:

50 * 2^x = 170

where x represents the number of doubling times. To solve for x, we can take the logarithm of both sides:

x = log(170/50) / log(2) ≈ 2.8074

Since we can't have a fraction of a doubling time, we round up to the nearest whole number, x = 3.

Therefore, it would take approximately 48 hours (3 doubling times * 16 hours per doubling time) for there to be 170 bacteria present.