To find the elasticity for the demand function $q = D(p) = \sqrt{460 - p}$, let's go through the process step-by-step.

Part (a) Find the elasticity formula $E(p)$:

1. Recall the Elasticity of Demand formula: $E(p) = -\frac{p}{q} \cdot \frac{dq}{dp}$

2. Differentiate the Demand Function $q = D(p) = \sqrt{460 - p}$ with respect to $p$: $\frac{dq}{dp} = \frac{d}{dp} \left( \sqrt{460 - p} \right) = \frac{-1}{2\sqrt{460 - p}}$

3. Substitute $q = \sqrt{460 - p}$ and $\frac{dq}{dp} = \frac{-1}{2\sqrt{460 - p}}$ into the elasticity formula: $E(p) = -\frac{p}{\sqrt{460 - p}} \cdot \frac{-1}{2\sqrt{460 - p}}$

4. Simplify the expression: $E(p) = \frac{p}{2(460 - p)}$

So, the elasticity of demand equation is: $E(p) = \frac{p}{2(460 - p)}$

Would you like to proceed with Part (b), where we calculate elasticity at $p = 119$, or need further details on this calculation?

Follow-up Questions

1. How does elasticity help determine consumer responsiveness to price changes?
2. What does it mean if the elasticity $E(p)$ is greater than, less than, or equal to 1?
3. How do we interpret the elasticity result in terms of demand being elastic, inelastic, or unit elastic?
4. How does differentiating the demand function aid in finding elasticity?
5. How would changes in the demand function affect the elasticity formula?

Tip

When calculating elasticity, always check if the demand function requires additional simplification before applying differentiation.