Answer: Therefore, there will be 15,625 bacteria after 72 hours.
Step-by-step explanation:
Let N(t) be the number of bacteria at time t. The rate of change of bacteria is proportional to the number of bacteria present, so we have:
dN/dt = kN
where k is the constant of proportionality.
Using the initial condition N(0) = 20, we can solve for k:
N(0) = 20
N(t) = N(0)e^(kt)
50 = 20e^(8k)
ln(50/20) = 8k
k = ln(5/2)/8
Now, we can find N(72):
N(72) = 20e^(72k)
N(72) = 20e^(9ln(5/2))
N(72) = 20(5/2)^9
N(72) = 15625
Therefore, there will be 15,625 bacteria after 72 hours.