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. Which of the following equations correctly models the ball's peak height, $h$ , in meters, after $b$ bounces? $\newline$ Choose $1$ answer: $\newline$ (A) $h=4\cdot0.79^{(b-1)}$ $\newline$ (B) $h=4\cdot0.79^{b}$ $\newline$ (C) $h=4-0.79\cdot b^{2}$ $\newline$ (D) $h=4\cdot(1-0.79\cdot b^{2})$

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Grade 7

Volume of cubes and rectangular prisms: word problems

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Q. 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. Which of the following equations correctly models the ball's peak height,

h

, in meters, after

b

bounces?

\newline

Choose

1

answer:

\newline

(A)

h=4\cdot0.79^{(b-1)}

\newline

(B)

h=4\cdot0.79^{b}

\newline

(C)

h=4-0.79\cdot b^{2}

\newline

(D)

h=4\cdot(1-0.79\cdot b^{2})

Understand the problem: Understand the problem. $\newline$ We need to find an equation that models the peak height of the ball after it bounces. The initial height is $4$ meters, and after each bounce, the ball reaches $79\%$ of the previous height.
Analyze the answer choices: Analyze the answer choices. $\newline$ We are given four different equations to choose from. We need to determine which equation correctly represents the situation where the height of the ball after each bounce is $79\%$ of the height of the previous bounce.
Evaluate the answer choices: Evaluate the answer choices. $\newline$ (A) $h=4\times0.79^{(b-1)}$ suggests that the initial bounce is not counted, which is incorrect because the initial height should be $100\%$ of the starting height. $\newline$ (B) $h=4\times0.79^{b}$ suggests that the height after the first bounce is $79\%$ of the initial height, which is correct. $\newline$ (C) $h=4-0.79\times b^{2}$ suggests a linear and quadratic decrease, which does not match the percentage decrease described. $\newline$ (D) $h=4\times(1-0.79\times b^{2})$ also suggests a quadratic decrease, which is incorrect.
Choose the correct equation: Choose the correct equation. $\newline$ The correct equation must start with the initial height of $4$ meters and then decrease by $79\%$ after each bounce. This is a geometric sequence where each term is $79\%$ of the previous term. The correct equation is the one that starts with the initial height and multiplies by $0.79$ raised to the power of the number of bounces.
Confirm the correct equation: Confirm the correct equation. $\newline$ Option (B) $h=4\times0.79^{b}$ is the correct equation because it starts with the initial height of $4$ meters and then multiplies by $0.79$ to the power of $b$ , which represents the number of bounces. This matches the description of the problem where the height after each bounce is $79\%$ of the previous height.