Soru
At a price of 2.24 per bushel, the supply of a certain grain is 7100 million bushels and the demand is 7800 million bushels. At a price of 2.35 per bushel, the supply is 7500 million bushels and the demand is 7700 million bushels. (A) Find a price supply equation of the form p=mx+b where p is the price in dollars and x is the supply in millions of bushels. (B) Find a price -demand equation of the form p=mx+b where p is the price in dollars and xis the demand in millions of bushels. (C) Find the equilibrium point. (D) Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system. (A) The price-supply equation is p=0.000275x+0.2875 (Type an exact answer.) (B) The price-demand equation is p=-0.0011x+10.808 (Type an exact answer.)
Çözüm
4.7
(244 Oylar)
Devrim
Elit · 8 yıl öğretmeni
Uzman doğrulaması
Cevap
(A) The price-supply equation is
(B) The price-demand equation is
(C) The equilibrium point is (7640, 2.11)(D) Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system.
Daha Fazla
## Step 1: Find the price-supply equationTo find the price-supply equation, we need to determine the slope and y-intercept of the line that represents the relationship between price and supply.### Slope formula:The slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
Using the given data points (7100, 2.24) and (7500, 2.35), we can calculate the slope:
Now, we can use the point-slope form of a linear equation to find the equation of the line:
Substituting the values, we get:
Simplifying, we have:
## Step 2: Find the price-demand equationSimilarly, we can find the price-demand equation by determining the slope and y-intercept of the line that represents the relationship between price and demand.Using the given data points (7800, 2.24) and (7700, 2.35), we can calculate the slope:
Using the point-slope form of a linear equation, we get:
Simplifying, we have:
## Step 3: Find the equilibrium pointThe equilibrium point is the point where the supply and demand curves intersect, meaning the price-supply equation is equal to the price-demand equation.Setting the two equations equal to each other, we have:
Solving for
, we get:
Substituting this value back into either equation, we can find the equilibrium price:
So, the equilibrium point is (7640, 2.11).## Step 4: Graph the equationsTo graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system, we can plot the lines on a graph with the x-axis representing the supply/demand in millions of bushels and the y-axis representing the price in dollars.The price-supply equation will be a line with a positive slope passing through the points (7100, 2.24) and (7500, 2.35).The price-demand equation will be a line with a negative slope passing through the points (7800, 2.24) and (7700, 2.35).The equilibrium point will be a point on both lines, representing the intersection of the supply and demand curves.