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Number of problems — 3
No calculator is allowed for these problems. 4. Water is pumped into an underground tank at a constant rate of 8 gallons per minute. Water leaks out of the tank
at the rate of t + 1 gallons per minute, for 0 ≤ t ≤ 120 minutes. At time t = 0, the tank contains 30 gallons of
water.
(a) How many gallons of water leak out of the tank from time t = 0 to t = 3 minutes?
(b) How many gallons of water are in the tank at time t = 3 minutes?
(c) Write an expression for A(t ), the total number of gallons of water in the tank at time t.
(d) At what time t, for 0 t 120, is the amount of water in the tank a maximum? Justify your answer. 5. Consider the curve given by xy 2  x 3 y = 6.
(a) Show that dy
3x 2 y − y 2
=
.
dx
2 xy − x 3 (b) Find all points on the curve whose xcoordinate is 1, and write an equation for the tangent line at each of
these points.
(c) Find the xcoordinate of each point on the curve where the tangent line is vertical. 6. Consider the differential equation dy
3x 2
= 2y .
dx
e (a) Find a solution y = f ( x ) to the differential equation satisfying f ( 0) = 1 .
2
(b) Find the domain and range of the function f found in part (a). END OF EXAMINATION Copyright © 2000 College Entrance Examination Board and Educational Testing Service. All rights reserved.
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 Fall '14

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