Question

In a lab experiment, 610 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 23 hours. How long would it be, to the nearest tenth of an hour, until there are 1040 bacteria present?​

Answer 1

To determine how long it would take for the number of bacteria to reach 1040 given an initial count of 610 and a doubling time of 23 hours, we can use the formula for exponential growth. The approximate time it would take is 7.1 hours.

Step-by-step explanation:

To determine how long it would take for the number of bacteria to reach 1040, we can set up an exponential growth equation. The initial number of bacteria is 610 and it doubles every 23 hours. We can use the formula A = P * (2^(t/n)), where A is the final amount, P is the initial amount, t is the time, and n is the doubling time.

Substituting the given values, we have 1040 = 610 * (2^(t/23)). To solve for t, we can take the logarithm of both sides: log(1040) = log(610) + (t/23) * log(2). Evaluating the logarithms using a calculator, we find t ≈ 7.1 hours.

Therefore, it would take approximately 7.1 hours for the number of bacteria to reach 1040.