The Amount Of Money In A Savings Account Increases At A Rate Of $225 Per Month. After Eight Months The Bank Account Has $4,580 In It. Y-1,400=56(x+26) Whose Function Has The Smaller Y-intercept

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The Amount of Money in a Savings Account Increases at a Rate of $225 per Month: A Mathematical Analysis

In this article, we will explore the concept of savings accounts and how the amount of money in them increases over time. We will use a mathematical equation to model this situation and compare it to another given function to determine whose function has the smaller y-intercept.

Let's start by analyzing the given information. The amount of money in the savings account increases at a rate of $225 per month. After eight months, the bank account has $4,580 in it. We can use this information to create a mathematical equation that represents the situation.

The equation is given as:

y - 1,400 = 56(x + 26)

Breaking Down the Equation

To understand this equation, let's break it down into its components.

  • y represents the amount of money in the savings account.
  • 1,400 is the initial amount of money in the account.
  • 56 is the rate at which the money increases per month.
  • x represents the number of months.
  • 26 is the number of months that have passed before the rate of increase starts.

Simplifying the Equation

To simplify the equation, we can start by isolating y.

y - 1,400 = 56(x + 26)

y = 56(x + 26) + 1,400

y = 56x + 1,456 + 1,400

y = 56x + 2,856

The y-Intercept

The y-intercept is the point at which the graph of the equation crosses the y-axis. In other words, it is the value of y when x is equal to 0.

To find the y-intercept, we can substitute x = 0 into the equation.

y = 56(0) + 2,856

y = 2,856

The Other Function

The other function is given as:

y = 56x + 2,856

Comparing the Functions

Now that we have both functions, we can compare them to determine whose function has the smaller y-intercept.

The first function is:

y = 56x + 2,856

The second function is:

y = 56x + 2,856

As we can see, both functions have the same y-intercept, which is 2,856.

In conclusion, the amount of money in a savings account increases at a rate of $225 per month. After eight months, the bank account has $4,580 in it. We used a mathematical equation to model this situation and compared it to another given function to determine whose function has the smaller y-intercept. We found that both functions have the same y-intercept, which is 2,856.

Mathematical analysis is a crucial tool in understanding various real-world phenomena. In this article, we used mathematical equations to model the situation of a savings account and compared it to another given function. This type of analysis helps us to understand the underlying principles and relationships between different variables.

The concept of savings accounts and the mathematical equations used to model them have real-world applications in finance and economics. Understanding how savings accounts work and how the amount of money in them increases over time can help individuals make informed decisions about their financial planning and investments.

Future research directions in this area could include exploring other mathematical models that can be used to represent savings accounts and comparing them to the one used in this article. Additionally, researchers could investigate the impact of different interest rates and compounding periods on the growth of savings accounts.

The following is a list of mathematical formulas and equations used in this article:

  • y = 56x + 2,856
  • y - 1,400 = 56(x + 26)
  • y = 56(x + 26) + 1,400
  • y = 56x + 1,456 + 1,400
  • y = 56x + 2,856
    Frequently Asked Questions: The Amount of Money in a Savings Account Increases at a Rate of $225 per Month

A: The initial amount of money in the savings account is $1,400.

A: The amount of money in the savings account increases at a rate of $225 per month.

A: The y-intercept of the equation y = 56x + 2,856 is 2,856.

A: To find the value of x when the amount of money in the savings account is $4,580, we can substitute y = 4,580 into the equation y = 56x + 2,856.

4,580 = 56x + 2,856

Subtracting 2,856 from both sides gives:

1,724 = 56x

Dividing both sides by 56 gives:

x = 31

So, the value of x when the amount of money in the savings account is $4,580 is 31.

A: To calculate the amount of money in your savings account, you can use the equation y = 56x + 2,856, where x is the number of months and y is the amount of money in the account.

For example, if you want to know the amount of money in your savings account after 8 months, you can substitute x = 8 into the equation:

y = 56(8) + 2,856

y = 448 + 2,856

y = 4,580

So, the amount of money in your savings account after 8 months is $4,580.

A: This concept has many real-world applications in finance and economics. For example, it can be used to calculate the interest earned on a savings account, the growth of an investment, or the impact of inflation on the value of money.

A: Yes, you can use this concept to compare different savings accounts. By using the equation y = 56x + 2,856, you can calculate the amount of money in each account after a certain number of months and compare the results.

A: One limitation of this concept is that it assumes a constant rate of increase, which may not be the case in real-world situations. Additionally, it does not take into account other factors that may affect the growth of a savings account, such as interest rates or fees.

A: Yes, you can use this concept to predict the future value of a savings account. By using the equation y = 56x + 2,856, you can calculate the amount of money in the account after a certain number of months and predict the future value.

However, it's essential to note that this concept assumes a constant rate of increase and does not take into account other factors that may affect the growth of a savings account. Therefore, the accuracy of the prediction may be limited.

In conclusion, the amount of money in a savings account increases at a rate of $225 per month. We used a mathematical equation to model this situation and compared it to another given function to determine whose function has the smaller y-intercept. We also answered some frequently asked questions related to this concept and discussed its real-world applications and limitations.