Question

How many days will it take a culture of bacteria to increase from 2000 to

50,000? Use k = 0.657.​

Answer 1

5 days

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)\\(50000)/(2000)=e^(0.657t)\\25=e^(0.657t)\\0.657t=\ln 25\\t=(\ln 25)/(0.657)=4.9\approx 5\,\,days`