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Ede4ka [16]
3 years ago
9

The height h(n) of a bouncing ball is an exponential function of the number n of bounces.

Mathematics
2 answers:
Digiron [165]3 years ago
5 0

Answer:

The height of a bouncing ball is defined by h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}.

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:

h = h_{o}\cdot r^{n-1}, n \in \mathbb{N}, 0 < r < 1 (1)

Where:

h_{o} - Height reached by the ball on the first bounce, measured in feet.

r - Decrease rate, no unit.

n - Number of bounces, no unit.

h - 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:

r = \frac{h_{1}}{h_{o}} (2)

Where h_{1} is the height reached by the ball on the second bounce, measured in feet.

If we know that h_{o} = 6\,ft and h_{1} = 4\,ft, then the expression for the height of the bouncing ball is:

h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}

The height of a bouncing ball is defined by h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}.

umka2103 [35]3 years ago
4 0

Answer:

9 (2/3) ² but insted of 2 its n

Step-by-step explanation:

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