Question
A bank charges a fee on savings accounts that are inactive for an extended period of time. The equation y=7500(0.97)^x
represents the value, y
, of one account that was left inactive for period of x
years.
What is the
y-intercept of the equation and what does it represent?
Responses
represents the value, y
, of one account that was left inactive for period of x
years.
What is the
y-intercept of the equation and what does it represent?
Responses
Answers
GPT-4o mini
The equation given is \( y = 7500(0.97)^x \). In this equation, \( y \) represents the value of the account after \( x \) years of inactivity, and \( 7500 \) represents the initial value of the account.
To find the \( y \)-intercept, we set \( x = 0 \) and calculate \( y \):
\[
y = 7500(0.97)^0
\]
Since any number raised to the power of 0 is 1, we have:
\[
y = 7500 \cdot 1 = 7500
\]
Thus, the \( y \)-intercept is \( 7500 \).
**Interpretation of the \( y \)-intercept:**
The \( y \)-intercept of \( 7500 \) represents the initial value of the savings account at the start of the observation period (when \( x = 0 \), meaning before any years of inactivity). This is the amount of money in the account before it has experienced any decline due to inactivity fees over time.
To find the \( y \)-intercept, we set \( x = 0 \) and calculate \( y \):
\[
y = 7500(0.97)^0
\]
Since any number raised to the power of 0 is 1, we have:
\[
y = 7500 \cdot 1 = 7500
\]
Thus, the \( y \)-intercept is \( 7500 \).
**Interpretation of the \( y \)-intercept:**
The \( y \)-intercept of \( 7500 \) represents the initial value of the savings account at the start of the observation period (when \( x = 0 \), meaning before any years of inactivity). This is the amount of money in the account before it has experienced any decline due to inactivity fees over time.