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Rocio drops a ball from a height of 4 meters. Rocio observes that each time the ball bounces, it reaches a peak height which is 79% of the previous peak height, as shown at left. Which of the following equations correctly models the ball's peak height, h, in meters, after b bounces?

Sagot :

The exponential equation that correctly models the ball's peak height, h, in meters, after b bounces is given by:

[tex]H(b) = 4(0.79)^b[/tex]

What is an exponential function?

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

In this problem:

  • Rocio drops a ball from a height of 4 meters, hence A(0) = 4.
  • Each time the ball bounces, it reaches a peak height which is 79% of the previous peak height, hence 1 - r = 0.79.

Thus, the equation is given by:

[tex]H(b) = 4(0.79)^b[/tex]

More can be learned about exponential equations at https://brainly.com/question/25537936

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