Pre-Calculus
Name: ___________________
Date: _____ / _____ / _______
Application of Linear Equations
1. The relationship between the Fahrenheit (F) and Celsius (C) temperatures scales is given by the
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equation F  C  32 .
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a. Sketch a graph of this equation, letting the horizontal axis be the C-axis and the vertical
axis be the F-axis.
b. What is the slope of this graph and what does it represent? What is the F-intercept and
what does it represent?
2. An economist models the market for wheat by the following equations:
Supply Equation
y  8.33 p  14.58
y  1.39 p  23.35
Demand Equation
Where p is the price per bushel (in dollars), and y is the number of bushels produced and sold (in
millions).
a. At what point is the price so low that no wheat is produced?
b. At what point is the price so high that no wheat is sold?
c. Draw the graph of the supply and demand lines in the same viewing rectangle and find the
equilibrium point. Estimate the equilibrium price and the quantities produced and sold at
equilibrium.
3. A small business buys a computer for $4,000. After 4 years the value of the computer is expected
to be $200. For accounting purposes, the business uses linear depreciation to assess the value of
the computer at a given time. This means that if V is the value of the computer at time t, then a
linear equation is used to relate V and t.
a. Find a linear equation that relates V and t.
b. Find the depreciated value of the computer 3 years from the date of purchase.
4. A small-appliance manufacturer finds that if he produces x toaster ovens in a month his production
cost is given by the equation y  6 x  3000 (where y is measured in dollars).
a. Sketch a graph of this linear equation.
b. What do the slope and y-intercept of the graph represent?
5. Biologists have observed that the chirping rate of crickets of a certain species is related to
temperatures, and the relationship appears to be nearly linear. A cricket produces 120 chirps per
minute at 70 oF and 168 chirps per minute at 80 oF.
a. Find the linear equation that relates the temperature t and the number of chirps per minute
n.
b. If the crickets are chirping at 150 chirps per minute, estimate the temperature.
6. A jet flew from New York to Los Angeles, a distance of 4200 km. The speed for the return trip
was 100 km/hr faster than the outbound speed. If the total trip took 13 hours, what was the speed
from New York to Los Angles?
7. An object thrown or fired straight upward at an initial speed of v0 ft/s will reach a height of h feet
after t seconds, where h and t are related by the formula h  16t 2  v0 t . Suppose that a bullet is
shot straight upward with an initial speed of 800 ft/s.
a. When does the bullet fall back to ground level?
b. When does it reach a height of 6400 ft?
c. When does it reach a height of 2 miles?
d. How high is the highest point the bullet reaches?
8. The fish population in a certain lake rises and falls according to the formula
F  1000(30  17t  t 2 )
Here F is the number of fish at time t, where t is measured in years since January 1 , 1997, when the fish
population was first estimated.
a. On what date will the fish population again be the same as on January 1, 1997?
b. By what date will all the fish in the lake have died?