Answer:
the relative growth rate k = ln( 8 )
Step-by-step explanation:
Given the data in the question;
Initial population = 61 cells
which divides into two cells every 20 minutes;
Now.
dy/dt = ky
where y(t) = y(0) [tex]e^{kt[/tex]
y(t) is the population of bacteria
t is time in hours
y(0) is initial population
we know that, Initial population y(0) = 61
time t = 20 min = ( 20 / 60 )hr = 1/3 hr
so, y(1/3) = 2( 61 ) = 122
Now,
y(t) = y(0) [tex]e^{kt[/tex]
y(1/3) = 61 [tex]e^{k\frac{1}{3}[/tex]
122 = 61 [tex]e^{k\frac{1}{3}[/tex]
divide both sides by 122
2 = [tex]e^{k\frac{1}{3}[/tex]
ln(2) = k × 1/3
k = 3ln(2)
k = ln( 2³ )
k = ln( 8 )
Therefore, the relative growth rate k = ln( 8 )
