Question
Zoe just lit a new candle and then let it burn all the way down to nothing. The length of the candle remaining unburned, in inches, can be modeled by the equation L, equals, 9, minus, 0, point, 5, t, commaL=9−0.5t, where tt represents the number of hours since the candle was lit. What is the yy-intercept of the equation and what is its interpretation in the context of the problem?
Answer
Attempt 1 out of 2
The yy-intercept of the function is
which represents
Answer
Attempt 1 out of 2
The yy-intercept of the function is
which represents
Answers
GPT-4o mini
To find the \( y \)-intercept of the equation \( L = 9 - 0.5t \), we need to evaluate the function when \( t = 0 \), as the \( y \)-intercept occurs when the independent variable (in this case, \( t \)) is equal to zero.
Substituting \( t = 0 \) into the equation:
\[
L = 9 - 0.5(0) = 9
\]
Thus, the \( y \)-intercept is \( 9 \).
### Interpretation in the context of the problem:
The \( y \)-intercept of 9 represents the initial length of the candle when it was first lit. In other words, when \( t = 0 \) hours (the moment the candle is lit), the length of the candle is 9 inches.
Substituting \( t = 0 \) into the equation:
\[
L = 9 - 0.5(0) = 9
\]
Thus, the \( y \)-intercept is \( 9 \).
### Interpretation in the context of the problem:
The \( y \)-intercept of 9 represents the initial length of the candle when it was first lit. In other words, when \( t = 0 \) hours (the moment the candle is lit), the length of the candle is 9 inches.