Answer :
To determine which equation describes the relationship between \( t \) (the time in seconds) and \( h \) (the leaf's height in feet), we need to analyze the situation step-by-step.
1. Initial Height:
- The leaf starts at a height of 72 feet.
2. Rate of Fall:
- The leaf is falling at a rate of \( 5.5 \) feet per second. This means that every second, the leaf drops 5.5 feet.
3. Equation Components:
- We need to form an equation that represents the height \( h \) of the leaf after \( t \) seconds.
- Given that the leaf falls, the height is decreasing over time. Therefore, the rate of fall (5.5 feet per second) should be represented with a negative slope.
4. Initial Height Setup:
- At \( t = 0 \) seconds, the height \( h \) is 72 feet. This gives us the starting point for our equation.
- As time increases, the height decreases according to the rate of fall.
5. Forming the Equation:
- The equation needs to show the decrease in height as time progresses.
- For every second \( t \), the leaf's height \( h \) decreases by \( 5.5t \) feet.
Combining these components, the equation should start at 72 feet and then subtract \( 5.5t \) feet for each second \( t \):
[tex]\[ h = -5.5t + 72 \][/tex]
This equation indicates that for each second \( t \), the height \( h \) is reduced by \( 5.5 \) feet from the initial height of 72 feet.
Given the options:
A. \( h = 5.5t + 72 \)
B. \( h = 5.5t - 72 \)
C. \( h = -5.5t + 72 \)
D. \( h = -5.5t - 72 \)
The correct equation is:
[tex]\[ h = -5.5t + 72 \][/tex]
Therefore, the correct option is:
C. [tex]\( h = -5.5t + 72 \)[/tex]
1. Initial Height:
- The leaf starts at a height of 72 feet.
2. Rate of Fall:
- The leaf is falling at a rate of \( 5.5 \) feet per second. This means that every second, the leaf drops 5.5 feet.
3. Equation Components:
- We need to form an equation that represents the height \( h \) of the leaf after \( t \) seconds.
- Given that the leaf falls, the height is decreasing over time. Therefore, the rate of fall (5.5 feet per second) should be represented with a negative slope.
4. Initial Height Setup:
- At \( t = 0 \) seconds, the height \( h \) is 72 feet. This gives us the starting point for our equation.
- As time increases, the height decreases according to the rate of fall.
5. Forming the Equation:
- The equation needs to show the decrease in height as time progresses.
- For every second \( t \), the leaf's height \( h \) decreases by \( 5.5t \) feet.
Combining these components, the equation should start at 72 feet and then subtract \( 5.5t \) feet for each second \( t \):
[tex]\[ h = -5.5t + 72 \][/tex]
This equation indicates that for each second \( t \), the height \( h \) is reduced by \( 5.5 \) feet from the initial height of 72 feet.
Given the options:
A. \( h = 5.5t + 72 \)
B. \( h = 5.5t - 72 \)
C. \( h = -5.5t + 72 \)
D. \( h = -5.5t - 72 \)
The correct equation is:
[tex]\[ h = -5.5t + 72 \][/tex]
Therefore, the correct option is:
C. [tex]\( h = -5.5t + 72 \)[/tex]
