For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We have two points through which the line passes:
We found the slope:
Substituting we have:
Thus, the equation is of the form:
We substitute one of the points and find the cut-off point:
Finally, the equation is:
ANswer:
Answer:
The height of a bouncing ball is defined by .
Step-by-step explanation:
According to this statement, we need to derive the expression of the height of a bouncing ball, that is, a function of the number of bounces. The exponential expression of the bouncing ball is of the form:
,
,
(1)
Where:
- Height reached by the ball on the first bounce, measured in feet.
- Decrease rate, no unit.
- Number of bounces, no unit.
- Height reached by the ball on the n-th bounce, measured in feet.
The decrease rate is the ratio between heights of two consecutive bounces, that is:
(2)
Where is the height reached by the ball on the second bounce, measured in feet.
If we know that and
, then the expression for the height of the bouncing ball is:
The height of a bouncing ball is defined by .