wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In a culture, the bacteria count is 100000. The number is increased by 10% in 2 hours. In how many hours will the count reach 200000, if the rate of growth of bacteria is proportional to the number present?

Open in App
Solution

Let the bacteria count at any time t be N.Given:dNdtα NdNdt=λN1NdN=λdtIntegrating both sides, we get1NdN=λdtlog N=λt+log C .....(1)Initially when t=0, then N=100000 Givenlog 100000=0+log Clog C=log 100000After 2 hours number increased by 10%Therefore, increased number=1000001+10%=110000Given: t=2, N=110000Putting t=2, N=110000 in (1), we getlog 110000=2λ+log 10000012log 1110=λSubstituting the values of log C and λ in (1), we getlog N=t2log 1110+log 100000 .....(2)Now,Let t=T when N=200000Substituting these values in (2), we get log 200000=T2log 1110+log 100000log 2=T2log 1110T=2log 2log1110 The count will reach 200000 in 2log 2log1110 hours.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Venn Diagrams
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon