h ( t) = −16t^2 +b The function h estimates an object’s height, in feet, above the ground t seconds after the object is dropped, where b is a constant. The function estimates that the object is 3,364 feet above the = 0 ground when it is dropped at t. Approximately how many seconds after being dropped does the function estimate the object will hit the ground?
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice B is correct. It’s given that the function h estimates that the object is 3,364 = 3,364 feet above the ground when it’s dropped at t 0. Substituting for 3,364=-16 0 2+ 3,364= h^th and 0 for t in the function h yields ^ h b, or b. 3,364 =-16 2+3,364 Substituting for b in the function h yields h^th t . When the object hits the ground, its height will be 0 feet above the ground. Substituting 0 =-16 2+3,364 0=-16 2+3,364 16 2 for h^th in h^th t yields t . Adding t to each 16 2=3,364 16 side of this equation yields t . Dividing each side of this equation by 2=210.25 yields t . Since the object will hit the ground at a positive number of seconds after it’s dropped, the value of t can be found by taking the positive =14.50 square root of each side of this equation, which yields t . It follows that the 14.50 function estimates the object will hit the ground approximately seconds after being dropped. 7.25 Choice A is incorrect. The function estimates that seconds after being -16 7.25 2+3,364 2,523 dropped, the object’s height will be ^ h feet, or feet, above the ground. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors. 43 SAT PRACTICE TEST #7 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2
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