Beginner Differential Equations problem

[SpiffyEh]

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

 

[rock.freak667]

the rate of growth of savings is proportional to its size with the proportionality constant k = .0025

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 v_0x and x₀)
x, then y=kx?

 

[SpiffyEh]

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?

 

[rock.freak667]

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?

yes something would b equal to kM(t),

? = kM(t)

what should go in place of the '?'

 

[SpiffyEh]

M(t) = dm/dt = km

 

[rock.freak667]

M(t) = dm/dt = km

Now can you solve

dM/dt = kM ?

 

[SpiffyEh]

Now can you solve

dM/dt = kM ?

It doesn't need to be solved, that's 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.