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December 20, 2014

December 20, 2014

Posted by **may** on Tuesday, January 27, 2009 at 11:38pm.

differentital equation

dx/dt = 1000+0.10x

initial condition

x(0) = 1000

A) solve the initial value problem for x as a function of t

B) about how many years will it take for the amount in your account to reach $ 100,000

[I know how to plug in for part , but can anyone help me on the part A to find t]

- Calculas HS -
**drwls**, Wednesday, January 28, 2009 at 12:32pmUse the method of separation of variables to solve the differential equation, and the initial condition x(0) = 1000 to get the cosnstant term. The resulting x(t) will have an exponential form.

Separation of variables will involve the integration of

dx/(1000+0.10x) = dt

The resulting equation will be an approximation that is valid only when t is an integral number of years. During the interim, the balance will be a stepwise function until the next deposit and interest payment is made.

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