This exercise uses the population growth model A certain cul

This exercise uses the population growth model. A certain culture of the bacterium Rhodobacter sphaeroides initially has 30 bacteria and is observed to double every 5 hours. (a) Find an exponential model n(t) = n_0 2^t/a for the number of bacterial in the culture after t hours. n(t) = (b) Estimate the number of bacteria after 15 hours (c) After ho many hours will the beacteria count reach 1 million?

Solution

Dear Student Thank you for using Chegg !! Given that population of bacteria doubles every 5 hours Abd initial population =30 bacteria P = P0 (2)^ kt P := Population at time t hours P0:- Initial Population k :- Rate of increase t:- Time elapsed in hours Now after 5 hours P = 2P0 => 2P0 = P0 2^5k 2 = 2^5k 2^(5k-1) = 1 =5k-1 = 0 k = 2/5 Hence P = P0 (2)^(2/5)t b) After 16 hours P = 30* (2)^(16*2/5) P = 2533.455 Bacterias c) Bacteria Count reaches 1000000 1000000 = 30 * (2) ^(2/5)t 33333.3333 = 2^(0.4t) Taking natural log both sides we get ln (3333.33) = 0.4t (ln(2)) 37.5616949 = t Hence time taken is 37.57 hours olution