Suppose initially there were three bacteria and now there are 384 bacteria. How much time has elapsed, a bacterial strain doubles its number every three minutes
384 = 3 * 2^(t/3) ... t in minutes
log(384 / 3) = (t / 3) log(2)
To find out how much time has elapsed, given that a bacterial strain doubles its number every three minutes, we can use the concept of exponential growth.
Let's break down the steps to find the answer:
1. Start with the initial number of bacteria: 3.
2. Determine the growth factor: Since the bacterial strain doubles its number every three minutes, the growth factor is 2.
3. Set up an equation using the exponential growth formula:
Final Number = Initial Number * (Growth Factor)^(Time / Growth Period)
where the Growth Period is the time it takes for doubling to occur.
4. Plug in the given values and solve for Time:
384 = 3 * (2)^(Time / 3)
5. Divide both sides of the equation by 3 to isolate the exponent:
128 = 2^(Time / 3)
6. Take the logarithm (base 2) of both sides to remove the exponent:
log2(128) = (Time / 3)
7. Simplify the left side by finding the logarithm of 128 to the base 2:
log2(128) = 7
8. Multiply both sides of the equation by 3 to solve for Time:
7 * 3 = Time
Time = 21
Therefore, it takes 21 minutes for the initial 3 bacteria to grow to 384 bacteria, given that the bacterial strain doubles its number every three minutes.