Question

A culture started with 2000 bacteria. after 2 hours it grew to 2400 bacteria. predict how many bacteria will be present after 10 hours. round your answer to the nearest whole number. P=Ae^kt

Answer 1

Explanation:

Answer 2

Answer: There will be 4977 bacteria present after 10 hours.

Explanation:

The exponential function for continuous growth in t years is given by :-

`P=Ae^(kt)` (i)

, where A = initial population, k= rate of growth.

As per given, A= 2000,

After t= 2 hours, P=2400

Put these values in (i), we get

`2400=2000e^(2k)\\\\\Rightarrow\ 1.2=e^(2k)`

Taking log on both sides

`\ln 1.2=2k\\\\\Rightarrow\ k=(\ln1.2)/(2)=(0.182321556794)/(2)\\\\\Rightarrow\ k\approx0.09116`

put value of A=2000, k= 0.09116 and t= 10 , we get

`P=2000e^(0.09116*10)\\\\=2000e^(0.9116)\\\\=2000*2.4883\\\\=4976.6\approx4977`

Hence, there will be 4977 bacteria present after 10 hours.