According to one economic model, the demand for gasoline is a linear function of price. If the price of gasoline is p # $3.10 pe
r gallon, the quantity demanded in a fixed period of time is q - 65 gallons. If the price is $3.50 per gallon, the quantity of gasoline demanded is 45 gallons for that period.
a) Find a formula for q (demand) in terms of p (price).
b) According to this model, at what price is the gas so expensive that there is no demand.
a) Find a formula for q (demand) in terms of p (price).
b) According to this model, at what price is the gas so expensive that there is no demand.
1 answer:
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Answer:
General Formulas and Concepts:
<u>Calculus</u>
Limits
Limit Rule [Variable Direct Substitution]:
L'Hopital's Rule
Differentiation
- Derivatives
- Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]:
Step-by-step explanation:
We are given the limit:
When we directly plug in <em>x</em> = 0, we see that we would have an indeterminate form:
This tells us we need to use L'Hoptial's Rule. Let's differentiate the limit:
Plugging in <em>x</em> = 0 again, we would get:
Since we reached another indeterminate form, let's apply L'Hoptial's Rule again:
Substitute in <em>x</em> = 0 once more:
And we have our final answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits