Answer:
5 days
Step-by-step explanation:
Given: bacteria to increase from 2000 to 50,000
To find: Number of days that a culture of bacteria will take to increase from 2000 to 50,000
Solution:
The growth of bacteria is represented by the equation: [tex]P(t)=P_0e^{kt}[/tex]
Here, t denotes time, k denotes growth rate and [tex]P_0[/tex] denotes initial population of bacteria.
Take [tex]P_0=2000[/tex], [tex]P(t)=50000[/tex] and [tex]k=0.657[/tex]
[tex]50000=2000e^{0.657t}\\\frac{50000}{2000}=e^{0.657t}\\25=e^{0.657t}\\0.657t=\ln 25\\t=\frac{\ln 25}{0.657}=4.9\approx 5\,\,days[/tex]
