Math 1a. Precalculus Worksheet.Fall 20051. Some friends are taking a long car trip. They are traveling east onRoute 66 from Flagstaff, AZ through New Mexico and Texas intoOklahoma.• L et f be the function that gives the number of miles traveled thours into the trip, where t = 0 denotes the beginning of the trip.For example, f(7) is the distance traveled seven hours into thetrip.• L et g be the function that gives the car’s speed t hours into thetrip, where t = 0 indicates the time at the beginning of the trip.For example, g(7) is the speed of the car seven hours into thetrip.Suppose that the car p asses a sign that reads “Entering Gallup, NewMexico,” h hours into the trip. Wr ite the following expressions usingfunctional notation wherever appropriate.(a) The car’s speed one hour before entering Gallup.(b) 10 miles an hour slower than the s peed of the car entering Gallup.(c) Half the time th at it took to reach Gallup.(d) The speed of the car 6 hours after reaching Gallup.(e) The distance traveled in th e first two hours of the trip.(f) The distance traveled in the second two hours of the trip.(g) The distance traveled in the second three hou rs of the trip.(h) The average speed traveled in the first five hours of travel.(i) The average speed between hour 6 and hour twelve of the trip.12. Using Problem 1 Interpret the following in words.(a) f(h + 2)(b)12f(h)(c) f12h(d) f(h − 2)(e) f(h) − 2(f) f (h) + 2(g) g(h + 2)(h) g(h) + 2(i) g(h) − 2(j)12g(h)(k)12g(h − 1)3. A certain menacing biological culture (aka The Blob) grows at a rateproportional to its size. When it arrived unnoticed one Wednesdaynoon in Chicago’s Loop, it weighed just 1 g. By 4:00 p.m. rush hour ,it weighed 4 g. The Blob has its “eye” on the Sears Tower, a tastymorsel weighing 3,000,000,000,000 g (i.e. 3 × 1012g). As soon as itweighs 1000 times as much (i.e. 3 × 1015g), The Blob intends to eatthe Sears Tower. By what time must The Blob be stopped ? WillFriday’s rush-hour commuters be delayed?4. The Bay of Fundy in Canada has the highest tides in the world. Thetidal range (that is, the difference between between low and high tides)is 16 m eters. There are two high tides every 24.8 hours. We can usethis information to model the height h of the water (in meters above sealevel) as a function of time t (in hours since midnight on a particularday) by the functionh(t) = A cos(Bt) + C.(a) What should the value of A be?(b) What should the value of B be?(c) What is the physical meaning of
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