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? Choose 1 answer: (A) h=4*0.79^((b-1)) (B) h=4*0.79^(b) (C) h=4-0.79*b^(2) (D) h=4*(1-0.79*b^(2))

Question

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? Choose 1 answer: (A)  h=4*0.79^((b-1)) (B)  h=4*0.79^(b) (C)  h=4-0.79*b^(2) (D)  h=4*(1-0.79*b^(2))

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. 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. 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. (A) h=4*0.79^((b-1)) suggests that the initial bounce is not counted, which is incorrect because the initial height should be 100% of the starting height. (B) h=4*0.79^(b) suggests that the height after the first bounce is 79% of the initial height, which is correct. (C) h=4-0.79*b^(2) suggests a linear and quadratic decrease, which does not match the percentage decrease described. (D) h=4*(1-0.79*b^(2)) also suggests a quadratic decrease, which is incorrect.Choose the correct equation: Choose the correct equation. 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. Option (B) h=4*0.79^(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.

Full solution

More problems from Volume of cubes and rectangular prisms: word problems

Related topics