Home
Class 12
MATHS
Bacteria grow at rate proportional to th...

Bacteria grow at rate proportional to the number of bacteria present in culture.If initially there are 100 bacteria and k is a constant of proportionality,show that the number of bacteria at time t is `100e^(kt)`.

Promotional Banner

Topper's Solved these Questions

  • Definite integration

    CHETANA PUBLICATION|Exercise Exercise|111 Videos

  • Differentiation

    CHETANA PUBLICATION|Exercise Exercise|127 Videos

Similar Questions

Explore conceptually related problems

The rate of increase in the numbers of bacteria culture is proportional to the number present.If initially there were 1000 bacteria and the number doubles in 1 hour,find the number of bacteria after a time of 2 1/2 hours.

The rate of growth of bacteria is proportional to the number present.If initially,there were 1000 bacteria and the number double in 1 hour,find the number of bacteria after 2 1/2 hours.Take (sqrt 2=1.414) .

The rate o growth of bacteria is proportional to the number present . If intially, there were 1000 bacteria and the number doubles in 1 hours. Find the number of bacteria after 2""1/2 hours . [ take sqrt 2 = 1.414]

Bacteria increases at the rate proportional to the number of bacteria present. If the original number N doubles in 3hours,find in how many hours the numbers of bacteria will be 4 N?

Bacteria multiply at the rate proportional to the number of bacteria present.If the original number N doubles in 3 hours,show that the number will be 4N in 6 hours.

The number of bacteria in a culture doubles every hour. If there were 50 bacteria originally in a culture, how many bacteria will be there at the end of 5th hour?

CHETANA PUBLICATION-DIFFERENTIAL EQUATIONS-EXERCISE
  1. An ice ball melts at the rate proportional to the amount of ice at any...

    Text Solution

    |

  2. The rate of decay of the mass of a radioactive substance at any time i...

    Text Solution

    |

  3. Bacteria grow at rate proportional to the number of bacteria present i...

    Text Solution

    |

  4. The order and degree of differential equation sqrt((1+(dy/dx)^2)=((d^2...

    Text Solution

    |

  5. The differential equation of y=c^2+c/x is

    Text Solution

    |

  6. x^2+y^2=a^2 is a solution of

    Text Solution

    |

  7. The differential equation of all circles having their centre on the y=...

    Text Solution

    |

  8. The differential equation y dy/dx+x=0 represents family of……..

    Text Solution

    |

  9. The solution of 1/x dy/dx=tan^(-1)x is……….

    Text Solution

    |

  10. The solution of (x+y)^2 dy/dx=1 is…………

    Text Solution

    |

  11. The solution of dy/dx=(y+sqrt(x^2-y^2))/x is

    Text Solution

    |

  12. The solution of dy/dx+y=cos x-sin x is

    Text Solution

    |

  13. The integrating factor of linear differential equation x dy/dx+2y=x^2 ...

    Text Solution

    |

  14. The solution of the differential equation dy/dx=sec x-y tan x is

    Text Solution

    |

  15. The particular solution of dy/dx=xe^(y-x) when y=0, x=0 is

    Text Solution

    |

  16. The decay rate of certain substance is directly proportional to the am...

    Text Solution

    |

  17. The order and degree of the differential equation d^3y/dx^3+(dy/dx)^4+...

    Text Solution

    |

  18. The order and degree of the differential equation [1+(dy/dx)^3]^(7/3=7...

    Text Solution

    |

  19. The order and degree of the differential equation sqrt(1+(dy/dx)^3)=(d...

    Text Solution

    |

  20. The order and degree of the differential equation of parabolas whose ...

    Text Solution

    |