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Functions : Real-Life Application Problems

1. Area of a painting. A rectangular painting with a width of x centimeters has an area of x2 _ 50x square centimeters.
Find a binomial that represents the length.

2. Amount of an investment. The amount of an investment of P dollars for t years at simple interest rate r is given by
A _ P _ Prt.
a) Rewrite this formula by factoring out the greatest common factor on the right-hand side.
b) Find A if $8300 is invested for 3 years at a simple interest rate of 15%.

Warm-Ups ▼
4. Demand for pools. Tropical Pools sells an aboveground model for p dollars each. The monthly revenue for this
model is given by the formula R(p)__0.08p2 _ Revenue is the product of the price p and the demand (quantity sold).
a) Factor out the price on the right-hand side of the formula.

b) Write a formula D(p) for the monthly demand.

c) Find D(3000).

d) Use the accompanying graph to estimate the price at which the revenue is maximized. Approximately how
many pools will be sold monthly at this price?
Figure for Exercise 100
0 2000 3000 4000
Price (dollars)
Revenue (thousandsof dollars)

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5. Area of a sail. The area in square meters for a triangular sail is given by A(x) _ x2 _ 5x _ 6.

a) Find A(5).

b) If the height of the sail is x _ 3 meters, then what is the length of the base of the sail?

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6. Worker efficiency. In a study of worker efficiency at Wong Laboratories it was found that the number of components
assembled per hour by the average worker t hours after starting work could be modeled by the formula N(t)__3t3 _ 23t2 _ 8t.

7. Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters,
then what are the lengths of the sides?
Figure for Exercise 74
10 m
x _ 2 m
x m

8. Throwing a wrench. An angry construction worker throws his wrench downward from a height of 128 feet with an
initial velocity of 32 feet per second. The height of the wrench above the ground after t seconds is given
by S(t)__16t2 _ 32t _ 128.

a) What is the height of the wrench after 1 second?

b) How long does it take for the wrench to reach the ground?

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Solution Summary

Real-Life application problems like area of a painting, amount of an investment, demand for pools, area of a sail, worker efficiency, rectangular stage and throwing a wrench has been solved using algebra.