Linear approximation of bus revenue

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Homework Help Overview

The problem involves analyzing the revenue function R(x) = 1.5x − 0.01x² for a bus company, specifically at the price point of x = 80 dollars. The focus is on understanding how a small increase in price affects revenue using linear approximation techniques.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the derivative of the revenue function and its implications for revenue changes. There is an exploration of the linear approximation formula and its similarity to the linear equation format y = mx + b.

Discussion Status

The discussion includes attempts to clarify the derivative's value and its significance in the context of revenue changes. Some participants express understanding of the linear approximation concept, while others engage in confirming their interpretations of the mathematical relationships involved.

Contextual Notes

Participants are working within the constraints of a homework assignment that requires the use of linear approximation without providing complete solutions. There is an emphasis on understanding the underlying concepts rather than arriving at a final answer.

bcahmel
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Homework Statement


If the price of a bus pass from Albuquerque to Los Alamos is set at x dollars, a bus company takes in a monthly revenue of R(x) = 1.5x − 0.01x2 (in thousands of dollars).

Suppose that x = 80. How will revenue be affected by a small increase in price? Explain using the Linear Approximation.


The Attempt at a Solution


first I took the derivative which is 1.5-0.02x. Then I plugged 80 in for x, so f'(x)=-0.1. Is this right? So the revenue will slightly decrease.
 
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so the linear approximation is
R(x) \approx R(x_0) +R'(x_0)(x - x_0)
 
ok, so its just like y=mx+b, sort of..
 
Which is why they call it a linear approximation...
 
yes, I get it now...thanks mark44
 

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