Home
Class 12
MATHS
A population grows at the rate of 5% per...

A population grows at the rate of 5% per year. If `x=x(t)` denotes the number of individuals in the population after t years, then the rate of change of x is equal to 5% of x. Form the desired differential equation .

Text Solution

Verified by Experts

The correct Answer is:
`(dx)/(dt)=(5)/(100)x`.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise EXERCISE 9 (d) Short Answer Type Questions|20 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise EXERCISE 9 (e) Short Answer Type Questions|5 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise EXERCISE 9 (c) Short Answer Type Questions|18 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Chapter test 4|12 Videos

  • INTEGRALS

    MODERN PUBLICATION|Exercise COMPETITION FILE|24 Videos

Similar Questions

Explore conceptually related problems

A population grows at the rate of 5% per year. Then the population will be doubled in :

A population grows at the rate of 8% per year. How long does it take for the population to double? Use differential equation for it.

A popular grows at the rate of 10% of the population per year. How long does it take for the population to doble ?

The population of a village increases at a rate of 5% every year. If the present population of the village is 5620, find the population after 1 year.

The population of a village increases at a rate of 5% every year. If the present population of the village is 5620, find the population after 1 year.

The population of a town increases at 5% per annum . Its present population is 16000. what will ne its population after 2 years?

The population of a city increases at the rate 3% per year. If at time t the population of city is p, then find equation of p in time t.

The population of a town is 125000. It is increasing at the rate of 2% per annum. What will be its population after 3 years?

MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-EXERCISE 9 (c) Long Answer Type Questions (I)
  1. Which of the following is a differential equation of the family of cur...

    Text Solution

    |

  2. Form the differential equation of the family of curves : y= A e^(2x)...

    Text Solution

    |

  3. Find the differential equation of the family of curves y=A e^(2x)+B...

    Text Solution

    |

  4. The differential equation for y=e^(x)(acosx+bsinx) is

    Text Solution

    |

  5. Obtain the differential equation by eliminating 'a' and 'b' from the e...

    Text Solution

    |

  6. Show that the differential equation of the family of circles having th...

    Text Solution

    |

  7. Find the differential equation of all the circles which pass thorou...

    Text Solution

    |

  8. Find the differential equation of all the circles which pass throug...

    Text Solution

    |

  9. Obtain the differential equation of the family of circles : with ce...

    Text Solution

    |

  10. Form the differential equation of the family of circles in the seco...

    Text Solution

    |

  11. Obtain the differential equation of the family of circles : having ...

    Text Solution

    |

  12. Form the differential equation of the family of circles in the firs...

    Text Solution

    |

  13. Find the order of the differential equation of the family of all circl...

    Text Solution

    |

  14. Find the differential equation of all parabolas whose axes are paralle...

    Text Solution

    |

  15. Form the differential equation of the family of parabolas having ve...

    Text Solution

    |

  16. The differential equation of all parabolas each of which has a latu...

    Text Solution

    |

  17. Show that the differential equation that represents the family of a...

    Text Solution

    |

  18. Form the differential equation of the family of ellipses having foc...

    Text Solution

    |

  19. Form the differential equation of the family of hyperbola having fo...

    Text Solution

    |

  20. A population grows at the rate of 5% per year. If x=x(t) denotes the n...

    Text Solution

    |