Modeling Bank Account Growth with Differential Equations

In summary, the conversation discusses a bank account that earns 4% interest per year and income from designing web pages for local businesses. The differential equation for the account's balance after t years is found, and it is also determined that with an initial balance of $10,000, the account will have a balance of $18,000 in 5 years, taking into account the added interest and income. There is also a hint given to use e^(1/5) to solve the problem without a calculator.
  • #1
lordy12
36
0
1. You have a bank account that earns 4% interest per year. You earn $4500 per year designing web pages for local businesses and spend $5000 buying CD's and computer games.
a.) Find differential equation that models account t years from now, A(t). b) If A(0) = 10,000 how much money will be in the account in 5 years?




Homework Equations





3. a. dA/dt = 4500t - 5000t b. 10000(1.04)^5 + 4500*5 - 5000*5. Is this correct? The problem for part b is that I can't use a calculator and the problem gives me a hint that e^(1/5) = 6/5/
 
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  • #2
You've not used the 4% interest yet though. That says that every year 4% of your money will be added on. Can you add this into the differential equations?
 

FAQ: Modeling Bank Account Growth with Differential Equations

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves variables and their rates of change, and is commonly used to model various natural phenomena in physics, engineering, and other fields.

2. What is the difference between an ordinary and a partial differential equation?

An ordinary differential equation involves only one independent variable, while a partial differential equation involves multiple independent variables. This means that the solutions to ordinary differential equations are functions, while the solutions to partial differential equations are usually functions of multiple variables.

3. What are some real-world applications of differential equations?

Differential equations are used to model many physical phenomena, such as the motion of objects under the influence of gravity, the flow of fluids through pipes, and the spread of diseases. They are also used in engineering to analyze and design systems, such as electrical circuits and control systems.

4. How do you solve a differential equation?

There are various methods for solving differential equations, depending on the type of equation and its complexity. Some common methods include separation of variables, substitution, and using integrating factors. Advanced techniques such as Laplace transforms and numerical methods are also used for more complicated equations.

5. Are there any limitations to using differential equations?

While differential equations are a powerful tool for modeling and solving problems, they do have some limitations. They may not always have exact solutions, and it can be challenging to find solutions for complex or non-linear equations. Additionally, the solutions obtained from differential equations may not always accurately reflect real-world situations due to simplifications and assumptions made in the modeling process.

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