Question 6 of 14 This test: 14 point(s) possible This question: 1 point(s) possibl Find the elasticity of demand $(E)$ for the given demand function at the indicated values of $p$. Is the demand elastic, inelastic, or neither at the indicated values? \[ q=407-0.2 p^{2} \] a. $\$ 20$ b. $\$ 36$ a. $E=$ (Type an integer or decimal rounded to the nearest thousandth as needed.) a. The demand is b. $E=$ (Type an integer or decimal rounded to the nearest thousandth as needed.) b. The demand is

Step 1 ：The elasticity of demand (E) is given by the formula: \(E = p \times \frac{dq}{dp} \div q\)

Step 2 ：The demand function is given by: \(q = 407 - 0.2p^2\)

Step 3 ：Taking the derivative with respect to p, we get: \(\frac{dq}{dp} = -0.4p\)

Step 4 ：For p = $20, we find q by substituting p = 20 into the demand function: \(q = 407 - 0.2(20)^2 = 307\)

Step 5 ：Then, we find \(\frac{dq}{dp}\) by substituting p = 20 into the derivative: \(\frac{dq}{dp} = -0.4(20) = -8\)

Step 6 ：Finally, we substitute these values into the formula for E: \(E = 20 \times (-8) \div 307 = -0.522\)

Step 7 ：\(\boxed{E = -0.522}\) for p = $20. Since the absolute value of E is less than 1, the demand is inelastic at this price.

Step 8 ：For p = $36, we find q by substituting p = 36 into the demand function: \(q = 407 - 0.2(36)^2 = 193\)

Step 9 ：Then, we find \(\frac{dq}{dp}\) by substituting p = 36 into the derivative: \(\frac{dq}{dp} = -0.4(36) = -14.4\)

Step 10 ：Finally, we substitute these values into the formula for E: \(E = 36 \times (-14.4) \div 193 = -2.692\)

Step 11 ：\(\boxed{E = -2.692}\) for p = $36. Since the absolute value of E is greater than 1, the demand is elastic at this price.