The demand for gasoline can be modeled as a linear function of price. If the price of gasoline is p = $3.10 per gallon, the quantity demanded in a fixed period is q = 75 gallons. If the price rises to $3.50 per gallon, the quantity demanded falls to 45 gallons in that period. (a) Find a formula for q in terms of p. q = 75р + 307.5 q = - 307.5p + 75 9 %3D 75р — 157.5 9%3 — 75р — 157.5 9 %3D 75р + 307.5 = O O O
The demand for gasoline can be modeled as a linear function of price. If the price of gasoline is p = $3.10 per gallon, the quantity demanded in a fixed period is q = 75 gallons. If the price rises to $3.50 per gallon, the quantity demanded falls to 45 gallons in that period. (a) Find a formula for q in terms of p. q = 75р + 307.5 q = - 307.5p + 75 9 %3D 75р — 157.5 9%3 — 75р — 157.5 9 %3D 75р + 307.5 = O O O
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:(b) Explain the economic significance of the slope of your formula.
The slope is m =
gallons per dollar, which tells us that the quantity of gasoline demanded in one time period
decreases by i
gallons for each $1 increase in price.
c) Explain the economic significance of the q-axis and p-axis intercepts.
If p = 0 then q
i
which means that if the price of gas were $0 per gallon, then the quantity demanded in
one time period would be
i
gallons per month. This means if gas were free, a person would want
gallons.
If q = 0 then p
i
. This tells us that (according to the model), at a price of $ i
per
gallon there will be no demand for gasoline. In the real world, this is
Transcribed Image Text:The demand for gasoline can be modeled as a linear function of price. If the price of gasoline is p = $3.10 per gallon, the quantity
demanded in a fixed period is q = 75 gallons. If the price rises to $3.50 per gallon, the quantity demanded falls to 45 gallons in that
period.
(a) Find a formula for q in terms of p.
Oq = – 75p + 307.5
q = – 307.5p + 75
Oq = 75p – 157.5
q = – 75p – 157.5
Oq = 75p + 307.5
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