Questions: Peyton has a savings account at First National Bank. The amount of money in the account grows exponentially. The table below shows the amount of money in her account each year. What does the y-intercept represent in the context of this problem?

Solution Steps

The $y$-intercept in the context of an exponential growth problem represents the initial amount of money in Peyton's savings account at the start of the observation period (i.e., at year 0). This is the value of the account before any growth has occurred.

In the context of exponential growth, the $y$-intercept represents the initial value of the quantity being measured. For Peyton's savings account, this means the amount of money in the account at the start of the observation period, or at year 0.

From the given data, the list of account values over the years is \([1000, 1100, 1210, 1331]\). The first value in this list, 1000, represents the initial amount in the account.

The $y$-intercept is the initial amount of money in Peyton's savings account. In mathematical terms, this is the value of the function at \(x = 0\), which is 1000.

Final Answer