Explanation Given information: It is provided that if the price of T-shirts are raised by $ 2 per month and the T-shirts are sold for $ 15 each where the demand for the T-shirts are provided with the help of formula q = 500 − 100 p 0.5 where q is the number of T-shirts which can be sold each month at a price of p dollars. Formula used: The steps for solving the related rate problem are: Step1: List the changing and related quantities followed by restating the problem in rate of change of terms. Step 2: Rewrite the problem using for the changing quantities for their derivatives. Step 3: If possible draw the diagram of the changing quantities and find an equation relating the changing quantities. Step 4: Differentiate with respect to the equation (s) in order to get rate of change in relating quantity. Step 5: Now substitute the values of the provided quantity and their derivative into the derived equation and solve them to get answer. Calculation: Consider the steps of the formula: The changing quantities are the number q of T-shirts sold per month and the price p per T-shirt. Since, the price of T-shirts is raised by $ 2 per month the T-shirts are sold for $ 15 each. Thus, the rate of change of price is 2 and when the price is $ 15 Therefore, d p d t = 2 at p = 15 Since, the rate at which the demands of T-shirts drop are to be determined. Thus, the above sentence can be rephrased as: What is the rate of change of q Thus, d q d t = ? Consider the relationship equation: q = 500 − 100 p 0.5 Differentiate the above equation with respect to t as, d q d t = d d t ( 500 − 100 p 0

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Videos

Question

Chapter 12.5, Problem 21E

To determine

To calculate: The rate at which the demand of T-shirts drop if the price of T-shirts are raised by $2 per month and the T-shirts are sold for $15 each where, the demand for the T-shirts are provided with the help of formula q=500−100p0.5 where, q is the number of T-shirts which can be sold each month at a price of p dollars.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.5, Problem 20E

Chapter 12.5, Problem 22E

Students have asked these similar questions

Find the value of t

Ezra has a base salary of $25,000 and earns 65% commission on vacuum cleaners. This means that for each vacuum cleaner he sells, he earns an additional amount that equals 65% of the price of the vacuum cleaner. To answer the following questions, use a model where S is Ezra’s total salary and v is the total dollar amount of his vacuum cleaner sales. What is the dollar amount of sales in vacuum cleaners Ezra will need to make in a year if he wants to earn $35,000? Round to the nearest cent.

Max used the equation y= 300(1.15) to predict how a. What is Max original credit card bill? much he has to pay on his credit card bill if he does not make any payments each month. a. ¿Qué es la factura máxima de la tarjeta de crédito original? x represents months y represents the amount he owes b. How much will money will Max owe if he does not pay off his balance for 5 months? Max usó la ecuación y 300(1.15)* para predecir cuánto tiene que pagar en la factura de su tarjeta de crédito si no hace ningún pago cada mes. !! b. ¿Cuánto dinero deberá Max si no paga su saldo durante 5 meses? x representa meses y representa la cantidad que debe Submit DELL

Chapter 12 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Solution Summary: The author calculates the rate at which the demand of T-shirts drops if the price is raised by 2 per month.

Concept explainers

Videos

Want to see the full answer?

Chapter 12 Solutions