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
The demand when p=55 can be found by substituting p=55 into the demand function D(p):
D(55) = 800/55 barrels.
Now, let's calculate:
D(55) = 14.545 barrels.
The decrease in demand if p rises to 56 can be estimated by calculating the difference in demand between the original price (p=55) and the new price (p=56):
Decrease in demand = D(55) - D(56).
Let's calculate:
Decrease in demand = 14.545 - (800/56) barrels.
As for the increase in demand if p is decreased to 54, we can estimate it by calculating the difference in demand between the original price (p=55) and the new price (p=54):
Increase in demand = D(54) - D(55).
Let's calculate:
Increase in demand = (800/54) - 14.545 barrels.
I hope the oil market doesn't get too grumpy with these price changes!
To find the demand when p=55, we need to substitute p=55 into the demand equation D(p)=800/p.
Substituting p=55 into the demand equation, we get:
D(55) = 800/55 = 14.545 barrels.
Thus, the demand when p=55 is approximately 14.545 barrels.
To estimate the decrease in demand if p rises to 56, we need to calculate the difference between the demand at p=55 and the demand at p=56.
Demand at p=56:
D(56) = 800/56 ≈ 14.286 barrels
Decrease in demand = D(55) - D(56) = 14.545 - 14.286 ≈ 0.259 barrels.
Thus, the decrease in demand if p rises to 56 is approximately 0.259 barrels.
To estimate the increase in demand if p is decreased to 54, we need to calculate the difference between the demand at p=54 and the demand at p=55.
Demand at p=54:
D(54) = 800/54 ≈ 14.815 barrels
Increase in demand = D(54) - D(55) = 14.815 - 14.545 ≈ 0.27 barrels.
Therefore, the increase in demand if p is decreased to 54 is approximately 0.27 barrels.
To find the demand when the price is $55 per barrel, we can substitute p = 55 into the demand function D(p) = 800/p.
So, D(55) = 800/55.
To calculate this, we divide 800 by 55, which gives us the demand when p = 55.
Now, let's calculate D(55) = 800/55.
D(55) ≈ 14.545 barrels
So, the demand when p = 55 is approximately 14.545 barrels.
To estimate the decrease in demand if the price rises to $56 per barrel, we need to calculate the difference between the demands at p = 55 and p = 56.
The decrease in demand = D(55) - D(56).
Now, we substitute p = 56 into the demand function D(p) = 800/p and subtract it from the demand at p = 55.
So, the decrease in demand = D(55) - D(56) ≈ 14.545 - (800/56).
To calculate this, we first find 800/56 and then subtract it from 14.545.
Let's calculate the decrease in demand ≈ 14.545 - (800/56).
Therefore, the decrease in demand ≈ 14.545 - 14.286 ≈ 0.259 barrels.
Finally, to estimate the increase in demand if the price is decreased to $54 per barrel, we need to calculate the difference in demands at p = 54 and p = 55.
The increase in demand = D(54) - D(55).
Now, we substitute p = 54 into the demand function D(p) = 800/p and subtract it from the demand at p = 55.
So, the increase in demand = D(54) - D(55) ≈ (800/54) - 14.545.
To calculate this, we first find 800/54 and then subtract 14.545 from it.
Let's calculate the increase in demand ≈ (800/54) - 14.545.
Therefore, the increase in demand ≈ 14.815 - 14.545 ≈ 0.270 barrels.
Hence, the demand when p = 55 is approximately 14.545 barrels, the decrease in demand if p rises to 56 is approximately 0.259 barrels, and the increase in demand if p is decreased to 54 is approximately 0.270 barrels.