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The quadratic function g models the depth, in meters, below the surface of the water of a seal t minutes after the seal entered the water during a dive. The function estimates that the seal reached its maximum depth of 302.4 meters 6 minutes after it entered the water and then reached the surface of the water 12 minutes after it entered the water. Based on the function, what was the estimated depth, to the nearest meter, of the seal 10 minutes after it entered the water? OP
Correct answer: 168 (parsed from the explanation — this source omits an answer key for this item)
Explanation
168 The correct answer is . The quadratic function g gives the estimated depth of the seal, g^th, in meters, t minutes after the seal enters the water. It’s given that 302.4 function g estimates that the seal reached its maximum depth of meters 6 minutes after it entered the water. Therefore, function g can be expressed in = -6 2+302.4 vertex form as g^th a^t h , where a is a constant. Since it’s also given 12 12 =0 that the seal reached the surface of the water after minutes, g^ h . 12 = -6 2+302.4 Substituting for t and 0 for g^th in g^th a^t h yields 0= 12-6 2+302.4 36 =-302.4 36 a^ h , or a . Dividing both sides of this equation by =-8.4 -8.4 = -6 2+302.4 gives a . Substituting for a in g^th a^t h gives =-8.4 -6 2+302.4 10 g^th ^t h . Substituting for t in g^th gives 10 =-8.4 10-6 2+302.4 10 =-8.4 4 2+302.4 g^ h ^ h , which is equivalent to g^ h ^ h , or 10 =168 g^ h . Therefore, the estimated depth, to the nearest meter, of the seal 10 168 minutes after it entered the water was meters. 48 SAT PRACTICE TEST #8 ANSWER EXPLANATIONS
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