Chapter4: Linear Functions
Section4.2: Modeling With Linear Functions
Problem 51SE: The Federal Helium Reserve held about 16 billioncubic feet of helium in 2010 and is being depleted...
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Transcribed Image Text:Step 3
Substitute this value of x in either the demand or the supply equation to get the corresponding value of p.
demand equation
p = 110 - 0.02( 100
100
= 110
2
108
108
Step 4
Check whether x = 100 and p = 108 satisfy the supply equation.
= 58 + 0.5
= 58 +
Therefore, the equilibrium point (x, p) is the ordered pair
(x, p) =
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Transcribed Image Text:Find the equilibrium point of the demand and supply equations.
Supply
p = 58 + 0.5x
Demand
p = 110 – 0.02x
Step 1
The equilibrium point is the ordered pair (x, p) that is obtained by solving the system of demand and supply
equations.
The two equations given are as follows.
p = 110 - 0.02x
demand equation
p = 58 + 0.5x
supply equation
In both the equations, p is represented in terms of x, so the method of substitution can be used to solve the
equations.
Substitute the expression forp given in the supply equation into the demand equation.
58
58
0.5
0.5 x = 110 - 0.02x
Step 2
Move the constants to one side of the equation. Remember to change the sign when moving a term from one
side to the other.
0.02x + 0.5 V
0.5 x = 110 - 58
58
Combine like terms.
0.52
0.52 x = 52
Solve for x by dividing both sides by the same number.
X = 100
100
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