Linear and Quadratic Function Models and Applications

Linear and Quadratic Function Models and Applications
Order 5897395
Linear and Quadratic Function Models and Applications
221. Suppose f(t) is the distance traveled at time t by a car moving at a constant
rate of speed of 65 miles per hour.
(A) Write a formula for f(t).
(B) What is the distance traveled at time hours?
222. A tank contains 2,000 gallons of water. Suppose water is drained from the
tank at a constant rate of 150 gallons per hour. Let f(t) be the amount of
water in the tank after t hours.
(A) Write a formula for f(t).
(B) How much water is in the tank at t = 3 hours? Hint: The amount of
water is decreasing, so the constant rate of change is negative.
223. A train is initially 245 miles from a city and moving toward the city at 60
miles per hour. Let f(t) be the distance from the city at time t.
(A) Write a formula for f(t).
(B) How far is the train from the city at t = 2.5 hours? Hint: The distance is
decreasing, so the constant rate of change is negative.
224. Hooke’s law states that F = –kx, where F is the force applied to a spring, x
is the distance that the spring stretches from its natural state, and k is the
constant of proportionality for the specific spring. Suppose for a certain
spring the constant of proportionality is 24,000 . Note: A dyne is a unit
of force in the centimeter-gram-second (CGS) system. Let F(x) be the force
(in dynes) applied when the spring stretches a distance of x centimeters.
(A) Write a formula for F(x).
(B) Find the force when the spring stretches 4 centimeters.
225. The monthly cost of driving a car includes both fixed and variable costs.
Suppose that the fixed monthly cost for driving a certain car is $121 and the
variable cost is 55.5 cents per mile driven. Let f(x) be the monthly cost (in
dollars) of driving this car for x miles.
(A) Write a formula for f(x).
(B) Find f(x) when x = 180 miles.
226. A farmer has 480 feet of fencing to enclose a rectangular pen for a donkey.
Let f(W) be the area of the rectangular pen expressed in terms of its width,
W.
(A) Write a formula for f(W).
(B) What dimensions for the rectangular pen will maximize the area for the
donkey?
227. The height (in feet) above the ground for an object that is projected
vertically upward with a velocity of 100 feet per second from an initial
height of 30 feet is given by h(t) = –16t
2 100t 30. Find the maximum
height of the object above the ground.
228. Suppose the monthly revenue R in thousands of dollars that a company
receives from producing x thousand boxes of designer watches is given by
R(x) = –4x
2 160x. How many boxes of designer watches should the
company produce each month to maximize R(x)?
229. Suppose a yearly cost function C in thousands of dollars is given by C(x) =
x
2 – 56x 3000. Find the minimum yearly cost.
230. Suppose an antique dealer determines that the value of a particular item
depends on its age according to the formula V(t) = – t
2 10t 800, where t
is measured in hundreds of years. At what age does the item have maximum
value?
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