1. scooby is standing on the edge of a 200-ft building. he throws a scooby snack vertically
upward. the function s(t) = -16° +64t+200 models the snack's height above the ground in
feet 1 seconds after it was thrown.
a. when does the snack reach its maximum height? what is the height?
b. how many seconds does it take for the snack to hit the ground?
c. find s(0) and describe what this represents.
d. if shaggy opens his mouth to catch the snack and his mouth is 6 ft from the ground, how
long before he will taste the snack in his open mouth?
2. two numbers sum to 16. find a pair whose product is as large as possible. what is the
maximum product?
3. you have 600 ft of fencing to enclose a rectangular plot of land that borders a river. if you do
not fence the river side, find the length and width of the plot that will maximize the area. what
is the largest area that can be enclosed?
4. a rain gutter is made from a metal sheet that is 12 in wide by folding up the edges to form
right angles. determine the depth of the gutter that will maximize its cross-sectional area and
allow the greatest amount of water to flow. what is the maximum cross-sectional area?
5. an airline carries 8000 passengers per month, each paying $50. a market survey indicates
that for every $1 increase in ticket price, the airline will lose 100 passengers. find the ticket
price that will maximize revenue. what is the maximum monthly revenue?
6. cherry trees yield 50 pounds of cherries per year if there are 30 or fewer trees per acre. for
each additional tree over 30, the annual yield per tree decreases by 1 pound due to overcrowding.
how many cherry trees should be planted to maximize yield. what is the maximum number of
pounds of cherries per acre?