Q In a culture, the bacteria count is 1,00,000 The number is increased by 10% in 2 hours - Maths - Differential Equations

Question

Q In a culture, the bacteria count is 1,00,000 The number is
increased by 10% in 2 hours In how many hours will the count reach
2,00,000, if the rate of growth of bacteria is proportional to the
number present?

Richa Kumari · Accepted Answer

A/q
dp/dt = kp
dp/p = k dt
Integrating we get
Log p = kt + c
After this folllow below image
Ans required is t1 as per image
<img src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5aa9787c873e4%20jpeg">

Q. In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?