Suppose demand is given by the equation \( Q=44-2 P \). Using the midpoint formula, what is the price elasticity of demand between the prices of 5 and 8 ? Include a negative sign if applicable, and round your answer to two decimal places.

To find the price elasticity of demand between the prices of 5 and 8 using the midpoint formula, we begin by calculating the quantity demanded at both prices. For \( P = 5 \): \[ Q = 44 - 2(5) = 44 - 10 = 34 \] For \( P = 8 \): \[ Q = 44 - 2(8) = 44 - 16 = 28 \] Now, we apply the midpoint formula for price elasticity of demand: \[ PE_d = \frac{\Delta Q / \text{Average } Q}{\Delta P / \text{Average } P} \] where \[ \Delta Q = Q_2 - Q_1 = 28 - 34 = -6 \] \[ \Delta P = P_2 - P_1 = 8 - 5 = 3 \] \[ \text{Average } Q = \frac{Q_1 + Q_2}{2} = \frac{34 + 28}{2} = 31 \] \[ \text{Average } P = \frac{P_1 + P_2}{2} = \frac{5 + 8}{2} = 6.5 \] Now, substituting these values into the formula: \[ PE_d = \frac{-6 / 31}{3 / 6.5} = \frac{-6}{31} \times \frac{6.5}{3} \] Calculating the right side: \[ PE_d = \frac{-6 \times 6.5}{31 \times 3} = \frac{-39}{93} \approx -0.419 \] Rounding to two decimal places, the price elasticity of demand is: \[ PE_d \approx -0.42 \]