Question

Bacteria in a culture increase at a rate proportional to the number of bacteria present. An initial population of 300 triples in 10 hours. If this pattern continues, find the number of bacteria present after one day.

Answer 1

Answer:

After 24 hours, there will be 4191 bacteria present in the culture.

Step-by-step explanation:

Initial number of bacteria = 300

amount in 10 hrs = 3 x 300 = 900

time taken = 10 hours

Bacterial growth is exponential, ans so we use the equation

N = N'$e^{kt}$

where N is the final amount

N' is the initial amount

k is the growth constant

t is the time

For this first case, we have

900 = 300 x $e^{k*10}$

3 = $e^{10k}$

take natural log of both sides, we'll have

ln 3 = ln $e^{10k}$

1.0986 = 10k

k = 1.0986/10 = 0.10986

using the growth constant above, we calculate for a day which is 24 hours

N = N'$e^{kt}$

N = 300 x $e^{0.10986*24}$

N = 300 x $e^{2.637}$

N = 300 x 13.97

N = 4191 bacteria