**Demand Function**

The demand function is given as Q = 10 - 2P, where Q represents the quantity demanded and P represents the price.

**Price Elasticity of Demand**

Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. It helps to understand how sensitive the demand is to changes in price.

The formula for price elasticity of demand (Ep) is:

Ep = (% change in quantity demanded) / (% change in price)

**Calculating Price Elasticity**

To find the price elasticity at the price of 5/2, we need to calculate the percentage change in quantity demanded and the percentage change in price.

First, we need to determine the initial quantity demanded and the initial price. At the price of 5/2, we substitute P = 5/2 into the demand function to find the initial quantity demanded:

Q = 10 - 2P
Q = 10 - 2(5/2)
Q = 10 - 5
Q = 5

So, the initial quantity demanded is 5.

Next, we need to determine the new quantity demanded and the new price. We assume that the price changes slightly from 5/2 to 5/2 + ΔP, resulting in a change in quantity demanded from 5 to 5 + ΔQ.

Now, we substitute P = 5/2 + ΔP into the demand function to find the new quantity demanded:

Q = 10 - 2P
Q = 10 - 2(5/2 + ΔP)
Q = 10 - 5 - 2ΔP
Q = 5 - 2ΔP

The change in quantity demanded, ΔQ, is given by:

ΔQ = (5 - 2ΔP) - 5
ΔQ = -2ΔP

The percentage change in quantity demanded is:

%ΔQ = (ΔQ / initial quantity demanded) * 100
%ΔQ = (-2ΔP / 5) * 100

Next, we calculate the percentage change in price:

%ΔP = (ΔP / initial price) * 100
%ΔP = (ΔP / 5/2) * 100
%ΔP = (ΔP / 5/2) * 100 * (2/2)
%ΔP = (2ΔP / 5) * 100

Finally, we substitute the percentage changes into the price elasticity formula:

Ep = (%ΔQ / %ΔP)
Ep = ((-2ΔP / 5) * 100) / ((2ΔP / 5) * 100)
Ep = (-2ΔP / 5) / (2ΔP / 5)
Ep = -2ΔP / 5 * 5 / 2ΔP
Ep = -2 / 2
Ep = -1

**Interpretation**

The price elasticity of demand at the price of 5/2 is -1. This means that a 1% increase in price will result in a 1% decrease in quantity demanded. The demand is considered to be unit elastic, indicating that demand is equally responsive to price changes.