A software entertainment company recently ran a holiday sale on its popular software program. Using data collected from the sale, it is possible to estimate. the demand corresponding to various discounts in the price of the software. Assuming that the original price was $\$ 38$, the demand for the software can be estimated by the function $q=3,775,000 p^{-2.843}$, where $p$ is the price and $q$ is the demand. Calculate and interpret the elasticity of demand.

Step 1 ：We are given a function that describes the demand as a function of price, which is \(q=3,775,000 p^{-2.843}\), where \(p\) is the price and \(q\) is the demand.

Step 2 ：The elasticity of demand is a measure of how much the quantity demanded of a good responds to a change in the price of that good. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Step 3 ：We can calculate the elasticity of demand by taking the derivative of the demand function with respect to price, and then multiplying by the ratio of price to quantity.

Step 4 ：By doing so, we find that the elasticity of demand is approximately 2.843.

Step 5 ：This means that a 1% increase in price would lead to a 2.843% decrease in quantity demanded, all else being equal.

Step 6 ：This indicates that the demand for the software is relatively elastic at this price point, meaning that consumers are quite sensitive to changes in price.

Step 7 ：Final Answer: The elasticity of demand at the original price of $38 is approximately \(\boxed{2.843}\).