1.Docking a BoatA boat is pulled toward a dock by means of a rope wound on a drum that is located5ft above the bow of the boat. If the rope is being pulled in at the rate of2ft/s, how fast (in ft/s) is the boat approaching the dock when it is17ft from the dock? (Round your answer to one decimal place.)

2.Radioactive DecayPhosphorus-32 (P-32) has a half-life of 14.2 days. If200g of this substance are present initially, find the amountQ(t) present aftertdays. (Round your growth constant to four decimal places.)

Q(t) =______

What amount (in grams) will be left after24.7days? (Round your answer to three decimal places.)

_____g

How fast (in grams per day) is the P-32 decaying whent=24.7? (Round your answer to three decimal places.)

______g/day

3.Consumers' SurplusThe demand function for a certain make of replacement cartridges for a water purifier is given by the following equation wherepis the unit price in dollars andxis the quantity demanded each week, measured in units of a thousand.

p=0.01x²0.2x+40

Determine the consumers' surplus if the market price is set at $5/cartridge. (Round your answer to two decimal places.)