Oil is being drained from an oil tank at a constant linear rate. Four hours after draining of the tank began, the volume of oil in the tank was 740 gallons, and seven hours after draining of the tank began, the volume was 545 gallons. Which of the following functions best models v(t), the volume of oil in the tank, in gallons, t hours after draining of the tank began?
A. v(t) = 740 - t
B. v(t) = 740 - 65t
C. v(t) = 1000 - 195t
D. v(t) = 1000 - 65t
Answer:D
Oil is being drained from an oil tank at a constant linear rate. Four hours after draining of the tank began, the volume of oil in the tank was 740 gallons, and seven hours after draining of the tank began, the volume was 545 gallons. Which of the following functions best models v(t), the volume of oil in the tank, in gallons, t hours after draining of the tank began?
A. v(t) = 740 - t B. v(t) = 740 - 65t C. v(t) = 1000 - 195t D. v(t) = 1000 - 65t
Explanation: D According to the question, if t = 4, then v(t) = 740. Plug 4 in for t in the answer choices and see if v(t) comes out to the target number 740. In (A) if t = 4, then v(t) = 740 - 4 = 736. Eliminate (A). In (B), if t = 4, then v(t) = 740 - 65(4) = 740 - 260 = 480. Eliminate (B). In (C), if t = 4, then v(t) = 1,000 - 195(4) = 1,000 - 780 = 220. Eliminate (C). The correct answer must therefore be (D).