Let's go step by step to solve this question based on the provided image.

Given:

• The demand function: $D(p) = 225 - 4p^2$
• The price: $p = 7$

The goal is to find the elasticity of demand $E(p)$ at $p = 7$ using the formula: $E(p) = \left| \frac{p}{q} \cdot \frac{dq}{dp} \right|$ where $q = D(p)$.

Step 1: Find $q$ at $p = 7$

We need to find $q = D(7)$: $D(7) = 225 - 4(7)^2 = 225 - 4(49) = 225 - 196 = 29$ So, $q = 29$.

Step 2: Differentiate $D(p)$ to find $\frac{dq}{dp}$

Now, differentiate the demand function $D(p) = 225 - 4p^2$: $\frac{dq}{dp} = -8p$ At $p = 7$, we have: $\frac{dq}{dp} = -8(7) = -56$

Step 3: Apply the elasticity formula

Now substitute the values into the elasticity formula: $E(p) = \left| \frac{7}{29} \cdot (-56) \right| = \left| \frac{-392}{29} \right| = \frac{392}{29} \approx 13.517241$ Rounding to six decimal places, we get: $E(p) \approx 13.517241$

Step 4: Determine the type of elasticity (part b)

Since $E(p) > 1$, the demand is elastic at this price.

Step 5: Determine the revenue strategy (part c)

For elastic demand, an increase in price will cause a greater decrease in quantity demanded, reducing total revenue. Therefore, to increase revenue, prices should be lowered.

Summary of Answers:

• (a) $E(p) \approx 13.517241$
• (b) The demand is elastic.
• (c) To increase revenue, lower prices.

Do you want further details on any step? Here are five related questions that might interest you:

1. What happens when demand is inelastic?
2. How do you interpret unitary elasticity of demand?
3. What are the factors that affect demand elasticity?
4. How can businesses use elasticity to maximize profits?
5. What are the limitations of using elasticity in real-world scenarios?

Tip: Elasticity helps businesses understand consumer behavior and set pricing strategies effectively.