1 3 6. (hours) R(1) (liters / hour) 1340 1190 950 740 700 Water is pumped into a tank at a rate modeled by W(1) = 2000e20 liters per hour for 0

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Chapter2: Second-order Linear Odes
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FT0C Free Response Problem 3
1
3
(hours)
R(1)
1340
1190
950
740
700
(liters / hour)
2/20
Water is pumped into a tank at a rate modeled by W(1) = 2000e720 liters per hour for 0 <1s 8, where t
is measured in hours. Water is removed from the tank at a rate modeled by R(1) liters per hour, where R is
differentiable and decreasing on 0<t< 8. Selected values of R(t) are shown in the table above. At time
I = 0, there are 50,000 liters of water in the tank.
(a) Estimate R'(2). Show the work that leads to your answer. Indicate units of measure.
(b) Use a left Riemann sum with the four subintervals indicated by the table to estimate the total amount of
water removed from the tank during the 8 hours. Is this an overestimate or an underestimate of the total
amount of water removed? Give a reason for your answer.
(c) Use your answer from part (b) to find an estimate of the total amount of water in the tank, to the nearest
liter, at the end of 8 hours.
(d) For 0 <t < 8, is there a time i when the rate at which water is pumped into the tank is the same as the rate
at which water is removed from the tank? Explain why or why not.
Transcribed Image Text:ICLOUD STORAGE IS FULL 2:09 PM Upgrade your storage to keep using iCloud. FT0C Free Response Problem 3 1 3 (hours) R(1) 1340 1190 950 740 700 (liters / hour) 2/20 Water is pumped into a tank at a rate modeled by W(1) = 2000e720 liters per hour for 0 <1s 8, where t is measured in hours. Water is removed from the tank at a rate modeled by R(1) liters per hour, where R is differentiable and decreasing on 0<t< 8. Selected values of R(t) are shown in the table above. At time I = 0, there are 50,000 liters of water in the tank. (a) Estimate R'(2). Show the work that leads to your answer. Indicate units of measure. (b) Use a left Riemann sum with the four subintervals indicated by the table to estimate the total amount of water removed from the tank during the 8 hours. Is this an overestimate or an underestimate of the total amount of water removed? Give a reason for your answer. (c) Use your answer from part (b) to find an estimate of the total amount of water in the tank, to the nearest liter, at the end of 8 hours. (d) For 0 <t < 8, is there a time i when the rate at which water is pumped into the tank is the same as the rate at which water is removed from the tank? Explain why or why not.
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