Demand for a certain kind of SUV obeys the following equation, D(x,y) = 16,000 – Vx – 15(0.4y – 10)3/2 where x is the price per car in dollars, y is the cost of gasoline per litre, and D is the number of cars. Suppose that the price of the car and the price of gasoline t years from now obey the following equations: x = 53,200 + 300t, y = 135 + 5V7 What will the rate of change of the demand be (with respect to time) 2 years from now?

Demand for a certain kind of SUV obeys the following equation, D(x,y) = 16,000 – Vx – 15(0.4y – 10)3/2 where x is the price per car in dollars, y is the cost of gasoline per litre, and D is the number of cars. Suppose that the price of the car and the price of gasoline t years from now obey the following equations: x = 53,200 + 300t, y = 135 + 5V7 What will the rate of change of the demand be (with respect to time) 2 years from now?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Demand for a certain kind of SUV obeys the following equation,
D(x,y) =
16,000 – Vx – 15(0.4y – 10)3/2
where x is the price per car in dollars, y is the cost of gasoline per litre, and D is the number of cars.
Suppose that the price of the car and the price of gasoline t years from now obey the following equations:
x = 53,200 + 300t,
y = 135 + 5V7
What will the rate of change of the demand be (with respect to time) 2 years from now?

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