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Beginner Differential Equations problem

  1. Jan 22, 2010 #1
    The problem is as follows:
    Assume interest in your savings account is compiunded continuously at a rate of .25%. Then the rate of growth of savings is proportional to its size with the proportionality constant k = .0025
    Write the differential equation that models this situation. Let M be the amount of savings at time, t (years). What type of growth is this? Is this equation linear?

    I'm not sure how to start this problem.... The whole concept is confusing me. If someone could show me how to go about doing this that would be very helpful. From this i can probably work on the other ones. Thanks
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 23, 2010 #2

    rock.freak667

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    Start with this statement

    If M(t) is the size, what is the rate of growth written in its differential form?

    Can you put that as being proportional to the the size and then use the fact that if y (in terms of v0x and x0)
    x, then y=kx?
     
  4. Jan 23, 2010 #3
    Well since M(t) is the amount of money at time t wouldn't the equation be km where k is the constant and m is the amount of money in the account? or am i thinking of this wrong?
     
  5. Jan 23, 2010 #4

    rock.freak667

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    yes something would b equal to kM(t),

    ??? = kM(t)

    what should go in place of the '???'
     
  6. Jan 23, 2010 #5
    M(t) = dm/dt = km
     
  7. Jan 23, 2010 #6

    rock.freak667

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    Now can you solve

    dM/dt = kM ?
     
  8. Jan 23, 2010 #7
    It doesn't need to be solved, thats actually all i needed for that part of the problem. I just thought it would be more complicated than that. I also got that its an exponential linear growth.
     
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