Answer :
To find the elasticity of demand E(p) using [tex]\(x = 84 - 0.3e^P\)[/tex], the expression is [tex]\(\frac{0.3e^P(84-0.3e^P)}{p}\)[/tex], derived from the price-demand equation.
To find the elasticity of demand (E(p)) using the price-demand equation [tex]\(x = f(p) = 84 - 0.3e^P\)[/tex], we use the formula:
[tex]\[E(p) = -\frac{p}{f'(p)} \times \frac{x}{p}\][/tex]
First, we need to find f'(p), the derivative of the demand function f(p) with respect to price p:
[tex]\[f(p) = 84 - 0.3e^P\]\[f'(p) = \frac{d}{dp} (84 - 0.3e^P)\][/tex]
Using the chain rule and the derivative of [tex]\(e^P\)[/tex], we get:
[tex]\[f'(p) = -0.3 \times e^P\][/tex]
Now, let's plug the values into the elasticity of demand formula:
[tex]\[E(p) = -\frac{p}{-0.3 \times e^P} \times \frac{x}{p}\]\[E(p) = \frac{0.3 \times e^P \times (84 - 0.3e^P)}{p}\][/tex]
This is the expression for E(p) in terms of p, representing the elasticity of demand.
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