1. Watson is filling a huge beaker. The water comes out of the faucet at a stead

Question

1. Watson is filling a huge beaker. The water comes out of the faucet at a steady rate. The beaker starts empty. He notices that after 5 seconds there is 420 cm3 of water in the beaker. a) How much water will be in the beaker after 12 seconds?






b) How much water will be in the beaker after 1427 seconds? after 3 seconds? (leave these unsimplified)






c) How much water goes into the beaker between time t = 3 sec and t = 3.1 sec?   How much goes in between time t = a and t = b?







d) Write an expression for how much water goes into the beaker during a period of time that is t seconds in duration. [We will sometimes use “t” to represent some change in t.]






2. Watson turns on the faucet (to perhaps a different setting than last time) and starts filling the beaker. Then he looks down and realizes that there must have already been some water in the beaker when he started filling it. After 5 seconds there is 420 cm3 of water in the beaker. After 11 seconds there is 840 cm3 of water in there. Let the A represent the varying amount of water in the beaker. a) How fast is the water coming out of the faucet? (remember to include units!)

b) Given a time increment of t sec, what is the corresponding A, that is, the change in the amount of water in the beaker over this time increment?







c) Using (5s, 420 cm3) as your “starting point,” determine how much water will be in the beaker after 7.2 seconds. (write it out—do not simplify)








d) How much water will be in the beaker after 1427 seconds? Again, use (5s, 420 cm3) as your “starting point,” and do not simplify or calculate.








e) Write a formula for the amount of water A in the beaker after t seconds.







f) Graph your formula, with t as the independent variable and A as the dependent one.

Explanation / Answer

1. a) after 5 sec, there is 420cm^3 of water in the beaker.

That means 420/5 = 84 cm^3/sec is the flow rate per second.

Amount of water after 12 sec = 84*12 = 1008 cm^3

b) after 1427 sec, 1427*12 = 17124cm^3.

after 3pi sec, 36pi cm^3

c) in time 3 sec and 3.1 = 12*(3.1 - 3) = 1.2 cm^3

in time a & b = 12(b-a) cm^3

d) Water going in the beaker during the time "t" = 12*t cm^3

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