Question

The generation time G for a particular bacteria is the time it takes for the population to double. The bacteria increase in population is shown by the formula G= (t)/(3.3log(base a)P)
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 the bacteria is 4.5 hours, how long will it take 4 of these bacteria to multiply into a colony of 7,525 bacteria? Round to the nearest hour.

Answer 1

Think the set up is like
4.5=t/(3.3log(base4)7525
4.5=t(3.3*ln7525/ln4=t/?
now I'm stuck don't know how to put in calculator @zepdrix

Answer 2

Solving for t gives us,
\[\huge t=4.5 \times 3.3 \log_4 7525\]Sure if wanna use natural logs,we can do that.
So using change of base formula gives us,\[\huge t=14.85 \times \frac{\ln 7525}{\ln 4}\]

Answer 3

\[\huge \ln(7525) \div \ln(4)\]Enter.
Press times key,\[\huge Ans \times 14.85\]