Question

How many days will it take a culture of bacteria to increase from 2000 to
50,000? Use k = 0.657.​

Answer 1

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: $P(t)=P_0e^{kt}$

Here, t denotes time, k denotes growth rate and $P_0$ denotes initial population of bacteria.

Take $P_0=2000$, $P(t)=50000$ and $k=0.657$

$50000=2000e^{0.657t}\\\frac{50000}{2000}=e^{0.657t}\\25=e^{0.657t}\\0.657t=\ln 25\\t=\frac{\ln 25}{0.657}=4.9\approx 5\,\,days$