Question

1. (a) If V'(t) is the rate at which water flows into a reservoir (in gal/min) at time t (in minutes), what does ???? V'(t) dt represent? (b) Suppose the number of honeybees in a colony is initially 100 bees and increases at a rate of n'(t) bees per week. What does 100 + ??¹² n'(t) dt represent? (c) Water leaks from the bottom of a storage tank at a rate of r(t) liters per minute. If the tank starts with 500 liters of water, write an expression that represents the amount of water left in the tank after 20 minutes. 2. A bacteria colony increases in size at a rate of 4.0553e¹.?? bacteria per hour. (a) Write an integral that represents the number of new bacteria in the colony after 3 hours. (b) Use n = 6 and left sums to evaluate the integral you found in part (a). (c) If the colony had 35 bacteria to start with, how many bacteria are in the colony after 3 hours? 3. A car with an initial velocity of 100 ft/s brakes at a constant rate (constant negative acceleration), coming to a stop in 8 seconds. Let t be the time in seconds after the car started to brake. (a) Sketch a graph of the car's velocity from t = 0 to t = 8 including labels. (b) Use the graph to compute the car's acceleration. Explain your computation. (c) How far did the car travel from t = 0 to t = 8? Give an expression in terms of integrals or derivatives to represent the distance and also compute the distance exactly.

          1. (a) If V'(t) is the rate at which water flows into a reservoir (in gal/min) at time t (in minutes), what does ???? V'(t) dt represent?
(b) Suppose the number of honeybees in a colony is initially 100 bees and increases at a rate of n'(t) bees per week. What does 100 + ??¹² n'(t) dt represent?
(c) Water leaks from the bottom of a storage tank at a rate of r(t) liters per minute. If the tank starts with 500 liters of water, write an expression that represents the amount of water left in the tank after 20 minutes.
2. A bacteria colony increases in size at a rate of 4.0553e¹.?? bacteria per hour.
(a) Write an integral that represents the number of new bacteria in the colony after 3 hours.
(b) Use n = 6 and left sums to evaluate the integral you found in part (a).
(c) If the colony had 35 bacteria to start with, how many bacteria are in the colony after 3 hours?
3. A car with an initial velocity of 100 ft/s brakes at a constant rate (constant negative acceleration), coming to a stop in 8 seconds. Let t be the time in seconds after the car started to brake.
(a) Sketch a graph of the car's velocity from t = 0 to t = 8 including labels.
(b) Use the graph to compute the car's acceleration. Explain your computation.
(c) How far did the car travel from t = 0 to t = 8? Give an expression in terms of integrals or derivatives to represent the distance and also compute the distance exactly.

1. (a) If V'(t) is the rate at which water flows into a reservoir (in gal/min) at time t (in minutes), what does ???? V'(t) dt represent?
(b) Suppose the number of honeybees in a colony is initially 100 bees and increases at a rate of n'(t) bees per week. What does 100 + ??¹² n'(t) dt represent?
(c) Water leaks from the bottom of a storage tank at a rate of r(t) liters per minute. If the tank starts with 500 liters of water, write an expression that represents the amount of water left in the tank after 20 minutes.
2. A bacteria colony increases in size at a rate of 4.0553e¹.?? bacteria per hour.
(a) Write an integral that represents the number of new bacteria in the colony after 3 hours.
(b) Use n = 6 and left sums to evaluate the integral you found in part (a).
(c) If the colony had 35 bacteria to start with, how many bacteria are in the colony after 3 hours?
3. A car with an initial velocity of 100 ft/s brakes at a constant rate (constant negative acceleration), coming to a stop in 8 seconds. Let t be the time in seconds after the car started to brake.
(a) Sketch a graph of the car's velocity from t = 0 to t = 8 including labels.
(b) Use the graph to compute the car's acceleration. Explain your computation.
(c) How far did the car travel from t = 0 to t = 8? Give an expression in terms of integrals or derivatives to represent the distance and also compute the distance exactly.

Added by Jeffrey B.

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