1. Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some
friends. His height as a function of time could be modeled by
,
where t is the time in seconds and h is the height in feet.
a. How long did it take for Jason to reach his maximum height?
b. What was the highest point that Jason reached?
2. If a toy rocket is launched vertically upward from ground level with an initial velocity of
128 feet per second, then its height h after t seconds is given by the equation
a. How long will it take the rocket to hit its maximum height?
b. What is the maximum height?
3. You and a friend are hiking in the mountains. You want to climb to a ledge that is 20
ft. above you. The height of the grappling hook you throw is given by the function
What is the maximum height of the grappling hook? Can you throw it high enough to
reach the ledge?
4. You are trying to dunk a basketball. You need to jump 2.5 ft. in the air to dunk the
ball. The height that your feet are above the ground is given by the function
What is the maximum height your feet will be above the ground? Will you be able to
dunk the basketball?
5. The number of bacteria in a refrigerated food is given by N(t)=20T 2 + 20T + 120,
where T is the termperature of the food in Celsius. At what temperature will the number
of bacteria be minimal?
6. For the years of 1983 to 1990, the number of mountain bike owners,m (in millions) in
the US can be approximated by the model m=0,337t2 – 2.265t + 3.962, where t
represents the number of years since 1980. In which year was the number of mountain
bike owners at a minimum?
7. A manufacturer of tennis balls has a daily cost of C(x) = 0.01x2 – 10x + 200 where C
is the total cost in dollars and x is the number of tennis balls produced. What number of
tennis balls will produce the minimum cost?
8. Your factory produced lemon-scented widgets. You know that each unit is cheaper,
the more you produce. But you also know that costs will eventually go up if you make
too many widgets, due to the costs of storage of the overstock. The guy in accounting
says your cost for producing x thousands of units a day can be approximated by the
formula C = 0.04x2 – 8.504x + 25302. Find the daily production level that will minimize
you costs.