Domanda del libro di testo
Calculate the derivative of the following functions.
y = csc ex
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Ch. 3 - Derivatives
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
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TOC.tableOfContents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Non è quello che usi tu?Cambia libro di testo
Capitolo 3, Problema 33a
Demand and elasticity Based on sales data over the past year, the owner of a DVD store devises the demand function , where D(p) is the number of DVDs that can be sold in one day at a price of p dollars.
a. According to the model, how many DVDs can be sold in a day at a price of \$10?
Guida verificata passo dopo passo1
Identify the demand function given in the problem: \( D(p) = 40 - 2p \).
Substitute the price \( p = 10 \) into the demand function.
Calculate \( D(10) = 40 - 2(10) \).
Simplify the expression to find the number of DVDs sold.
Interpret the result to understand how many DVDs can be sold at the price of \$10.
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Demand Function
A demand function expresses the relationship between the price of a good and the quantity demanded by consumers. In this case, the function D(p) = 40 - 2p indicates that as the price (p) increases, the quantity of DVDs sold (D) decreases. This linear relationship helps predict sales at different price points.
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Percorso guidato
06:21
Properties of Functions
Elasticity of Demand
Elasticity of demand measures how sensitive the quantity demanded is to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. Understanding elasticity helps businesses make informed pricing decisions to maximize revenue.
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04:18Maximizing Profit & Revenue
Substitution and Revenue Maximization
Substitution refers to how consumers may switch to alternative products as prices change. For the DVD store, if prices rise significantly, customers might choose digital streaming instead. Revenue maximization occurs when the price is set at a level where the product's demand is balanced with consumer willingness to pay, ensuring optimal sales and profit.
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04:18Maximizing Profit & Revenue
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Based on sales data over the past year, the owner of a DVD store devises the demand function D(p) = 40 - 2p, where D(p) is the number of DVDs that can be sold in one day at a price of p dollars.
For what prices is the demand elastic? Inelastic?
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Domanda del libro di testo
Based on sales data over the past year, the owner of a DVD store devises the demand function D(p) = 40 - 2p, where D(p) is the number of DVDs that can be sold in one day at a price of p dollars.
Find the elasticity function for this demand function.
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