Some banks chargea fee on saving accounts that are left inactive for an extended period of time. The equation `y=5,000(0.98)^(x)` represents the value, y, of one account that was left inactive for a period of x years. What is the y-intercepts of this equation and what does it represent?

Options

A. 0.98 the percent of money in the account initially
B. 0.98, the percent of money in the account after x years
C. 5,000, the amount of money in the account initially
D. 5,000, the amount of money in the account after x years.

Answer

To find the y-intercept of the equation \( y = 5000(0.98)^x \) and understand its significance, we will follow these steps:

### Step 1: Identify the equation
The given equation is:
\[ y = 5000(0.98)^x \]

### Step 2: Determine the y-intercept
The y-intercept occurs when \( x = 0 \). To find the y-intercept, we substitute \( x = 0 \) into the equation.

### Step 3: Substitute \( x = 0 \)
Substituting \( x = 0 \) into the equation:
\[ y = 5000(0.98)^0 \]

### Step 4: Simplify the expression
We know that any number raised to the power of 0 is 1. Therefore:
\[ (0.98)^0 = 1 \]
Now, substituting this back into the equation:
\[ y = 5000 \times 1 \]
\[ y = 5000 \]

### Step 5: Interpret the y-intercept
The y-intercept \( y = 5000 \) represents the initial value of the account when it was first opened (i.e., at \( x = 0 \)). This means that the account started with a balance of $5000.

### Final Answer
The y-intercept of the equation is \( 5000 \), which represents the initial amount in the savings account.

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