SAT question 100030d9 (Nonlinear Functions)

Question

A rubber ball bounces upward one-half the height that it falls each time it hits the ground. If the ball was originally dropped from a distance of 20.0 feet above the ground, what was its maximum height above the ground, in feet, between the third and fourth time it hit the ground?

College Board · Accepted Answer

The correct answer is 5/2,2.5,2.50. The correct answer is 5/2 . After hitting the ground once, the ball bounces to 20.0 ÷ 2 = 10.0 feet. After hitting the ground a second time, the ball bounces to 10.0 ÷ 2 = 5.0 feet. After hitting the ground for the third time, the ball bounces to 5.0 ÷ 2 = 2.5 feet. Note that 5/2, 2.5, and 2.50 are examples of ways to enter a correct answer.

CookSAT · Answer

Note: h(n) gives the maximum height after the nth hit, so evaluate h(3) for the bounce before the fourth hit.

1davien · Answer

the f(4) was kindof unnecessary, since looking at the function, its obviously decreasing, meaning the highest value between 3 and 4 will be f(3), but overall still gets the answer

Explanation

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Student discussion

SAT Question 100030d9: Nonlinear Functions answer and explanation with Desmos solution

Explanation

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Student discussion