the generation time g for a particular bacterium is the time it takes for a populations to double. the bacteria increase in population is shown by the formula G=t/3.3logaP, where t is the time period of the population increase, a is the number of bacteria at the beginning of the time period, and P is the number of bacteria at the end of the time period. if the generation time for bacteria is 4.5 hours, how long will it take 4 of these bacteria to multiply into a colony of 7525 bacteria? round to the nearest hour.
To find the time it takes for 4 bacteria to multiply into a colony of 7525 bacteria, we can use the formula for generation time:
G = t/3.3*log(a/P)
First, let's find the value of log(a/P):
log(a/P) = log(4/7525)
Next, let's substitute this value into the formula:
4.5 = t/3.3 * log(4/7525)
To isolate t, we can multiply both sides of the equation by 3.3:
4.5 * 3.3 = t * log(4/7525)
14.85 = t * log(4/7525)
Now, let's solve for t by dividing both sides of the equation by log(4/7525):
14.85 / log(4/7525) = t
Using a calculator to find the value of log(4/7525), we get approximately -3.624
14.85 / -3.624 ≈ -4.091
To round to the nearest hour, we can round -4.091 to -4.
Therefore, it will take approximately 4 hours for 4 bacteria to multiply into a colony of 7525 bacteria.