Question

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

Answer 1

the answer is 100% because it growth just double

Answer 2

Answer:

14.54 Hrs

Step-by-step explanation:

the rate of growth of bacteria is proportional to the number present

=> increase is compounding

Present count = 100000

number increased by 10 % in 2 hrs

200000 = 100000 ( 1 + 10/100)^(T/2)

=> 2 = (1.1)^(T/2)

Taking log both sides

log2 = (T/2) Log(1.1)

=> 0.301 = (T/2)(0.04139)

=> T = 0.602/0.04139

=> T = 14.54 Hrs