The demand for a commodity generally decreases as the price is raised. Suppose that the demand for oil (per capita per year) is D(p)=800/p barrels, where p is the price per barrel in dollars. Find the demand when p=55. Estimate the decrease in demand if p rises to 56 and the increase in demand if p is decreased to 54.
The demand D(55) = .
The decrease in demand = barrels.
The increase in demand = barrels.
To find the demand when p=55, we substitute p=55 into the demand function D(p)=800/p barrels:
D(55) = 800/55
D(55) ≈ 14.545 barrels (rounded to three decimal places)
The demand when p=55 is approximately 14.545 barrels.
To estimate the decrease in demand if p rises to 56, we need to find the difference in demand between p=55 and p=56. We can do this by subtracting the demand at p=56 from the demand at p=55:
Decrease in demand = D(55) - D(56)
Substituting the values into the demand function, we get:
Decrease in demand = 800/55 - 800/56
To estimate the increase in demand if p is decreased to 54, we need to find the difference in demand between p=54 and p=55. We can do this by subtracting the demand at p=55 from the demand at p=54:
Increase in demand = D(54) - D(55)
Substituting the values into the demand function, we get:
Increase in demand = 800/54 - 800/55
Now you can calculate the decrease and increase in demand by evaluating these expressions.