Final answer:
At a new price of $3.15 per gallon and a price elasticity of demand of 0.5, we can expect that the quantity of gas sold would decrease from the initial 5,000 gallons to 4,875 gallons.
Step-by-step explanation:
When the price of gasoline rises from $3.00 to $3.15 per gallon and considering the price elasticity of demand for gasoline is 0.5, we can calculate the impact on the quantity demanded using the elasticity formula. The formula for percentage change in quantity demanded is:
Percentage change in quantity demanded = (Price elasticity of demand) x (Percentage change in price)
To find the percentage change in price:
((New Price - Original Price) / Original Price) x 100 = ((3.15 - 3.00) / 3.00) x 100 = 5%
Using the price elasticity of demand, we now calculate the expected percentage change in quantity demanded:
(0.5) x (5%) = 2.5%
The calculated percentage signifies the reduction in quantity demanded. Since a 2.5% decrease in the quantity demanded from the initial 5,000 gallons is expected, we find the new quantity:
(Quantity x (1 - (Percentage change in quantity demanded / 100))) = 5,000 x (1 - 0.025) = 5,000 x 0.975 = 4,875 gallons
Hence, at a price of $3.15 per gallon, it is expected that 4,875 gallons of gas will be sold.