Final answer:
To find the elasticity of demand at a price of $10, substitute the price into the demand function to find the quantity. Then calculate the percentage change in quantity and use it to calculate the elasticity of demand using the formula % change in quantity / % change in price.
Step-by-step explanation:
To find the elasticity of demand at a price of $10, we need to calculate the percentage change in quantity when the price changes.
The elasticity of demand formula is % change in quantity / % change in price. Given the demand function is D(p) = 400 - 3p², we can find the quantity at a price of $10 by substituting p = 10 into the demand function:
D(10) = 400 - 3(10)² = 400 - 300 = 100.
Then, we can calculate the percentage change in quantity as:
% change in quantity = (100 - quantity at the original price) / quantity at the original price.
After calculating the percentage change in quantity, we can calculate the elasticity of demand using the formula mentioned earlier.