The income that a company receives from selling an item is called the revenue. Production decisions are based, in part, on howrevenue changes if the quantity sold changes; that is, on the rate of change of revenue with respect to quantity sold. Suppose acompany's revenue, in dollars, is given by R (q) = 100q – 10q², where q is the quantity sold in kilograms.(a) Calculate the average rate of change of R with respect to q over the intervals 1

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(a) Calculate the average rate of change of R with respect to q over the intervals 1 < q< 2 and 2 < q < 3. Average rate of change dollars/kg of revenue for 1 < qs2 Average rate of change of revenue for 2 < q< 3 dollars/kg

(a) Calculate the average rate of change of R with respect to q over the intervals 1 < q< 2 and 2 < q < 3. Average rate of change dollars/kg of revenue for 1 < qs2 Average rate of change of revenue for 2 < q< 3 dollars/kg

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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Exponential Growth Model

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Question

The income that a company receives from selling an item is called the revenue. Production decisions are based, in part, on how
revenue changes if the quantity sold changes; that is, on the rate of change of revenue with respect to quantity sold. Suppose a
company's revenue, in dollars, is given by R (q) = 100q – 10q², where q is the quantity sold in kilograms.
(a) Calculate the average rate of change of R with respect to q over the intervals 1 <q<2 and 2 <q< 3.
Average rate of change
dollars/kg
of revenue for 1 < q<2
Average rate of change
dollars/kg
of revenue for 2 < q<3
eTextbook and Media
(b) By choosing small values for h, estimate the instantaneous rate of change of revenue with respect to change in quantity at
q = 5 kilograms.
Instantaneous rate of change
i
dollars/kg
of revenue at q
5 kilograms

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