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Business Calculus Other Bases & Elasticity of Demand

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**3.5 The Exponential Function**

Know your facts for Know the graphs: A horizontal asymptote on one side at y = 0. Through the point (0,1) Domain: (-∞, ∞) Range: (0, ∞) a > < a < 1

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**2. Evaluate exponential functions by calculator.**

3. Differentiate : 4. Differentiate exponential functions using the sum/difference, coefficient, product, quotient, or chain rule.

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**Logarithmic Function Know your facts for**

Know the graph: A vertical asymptote on one side of the x axis at x = 0. Through the point (1,0). Domain: (0, ∞) Range: (-∞, ∞) a > < a < 1

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**2. Evaluate logarithmic functions by calculator.**

3. Change of Base formula: 4. Differentiate : 5. Differentiate exponential functions using the sum/difference, coefficient, product, quotient, or chain rule.

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3.6 Elasticity of Demand Given a demand function D(x) (quantity, also called q) where x is the price of an item, we want to determine how a small percentage increase in price affects the demand for the item. Percent change in price: (given as a decimal) Percent change in quantity: (given as a decimal) E(x) is the negative ratio of percent change in quantity to percent change in price.

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**For example: if a small increase in price causes a larger decrease**

in demand, this could result in a decrease in revenue. (Bad for business) In this case, E(x) would be a number > 1, and the demand is called elastic. On the other hand, a small increase in price may cause a smaller decrease in demand, resulting in an increase in revenue. Here, E(x) would be a number < 1, and the demand is called inelastic. If a percent change in price results in an equal percent change in demand, E(x) = 1, and demand is unit elastic.

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**Calculus & Elasticity and Revenue**

Using calculus, and taking the limit as ∆x → 0, we can show that We will use this formula for elasticity to find the elasticity of demand for a given demand function D(x), and to calculate elasticity at various prices.

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**Revenue is related to elasticity since R(x) = price * demand.**

If demand is inelastic, a small increase in price will result in an increase in revenue. If demand is elastic, a small increase in price will result in an decrease in revenue. If demand is unit elastic, the current price represents maximum revenue.

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MR. REY BELEN PRICE ELASTICITY OF SUPPLY. Supply Price and Quantity Demanded are directly related to each other. An increase in price causes the quantity.

MR. REY BELEN PRICE ELASTICITY OF SUPPLY. Supply Price and Quantity Demanded are directly related to each other. An increase in price causes the quantity.

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