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shad0w0f3vil
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ok i understand that, we did that sort of thing in class last week. I will look at that... thanks
Personal Wealth Model using DE's
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SUMMARY
The forum discussion centers on developing a mathematical model for personal wealth using the differential equation dW/dt=(1-p)(s-n+rW), where s represents salary, W(t) denotes wealth over time, r is the interest rate, n is necessary expenses, and p is the proportion of income spent on luxuries. Participants clarify that the equation requires integration rather than differentiation to derive the wealth function W(t)=((s-n)/r)(e^((1-p)rt)-1). The conversation emphasizes the importance of understanding initial conditions and the correct application of integration techniques, particularly in handling linear functions.
PREREQUISITES- Understanding of differential equations, specifically first-order linear equations.
- Familiarity with integration techniques, including integration of linear functions.
- Knowledge of mathematical modeling concepts related to personal finance.
- Basic understanding of exponential functions and their applications in growth models.
- Study methods for solving first-order linear differential equations.
- Learn about initial value problems and their significance in mathematical modeling.
- Explore the application of exponential growth models in finance.
- Investigate the implications of varying the parameters s, n, r, and p on wealth accumulation.
Students in mathematics or finance, educators teaching differential equations, and anyone interested in personal wealth modeling and financial planning.