Questions
ECON6003/ECON6703 Mathematical Methods of Econ Analysis Assignment 2
Numerical
The rate of consumption of a particular good is given by the differential equation 𝑑 𝑄 𝑑 𝑡 = 1560 𝑒 0.012 𝑡 . We know that Q(0)=0, that is Q=0 when t=0. Find Q(10) Note 1: There is an error margin of 5 in this question. That is, if the answer is 112.24, then any number in the interval [107.24, 117.24] will be accepted as correct. Note 2: Note: Just write the number in the space provided below. For example, if Q(10)= 6.6, then just write: 6.6
View Explanation
Verified Answer
Please login to view
Step-by-Step Analysis
We start with the given differential equation dQ/dt = 1560 e^{0.012 t}. To find Q(t), integrate with respect to t:
Q(t) = ∫ 1560 e^{0.012 t} dt = 1560 * (1/0.012) e^{0.012 t} + C = 130000 e......Login to view full explanationLog in for full answers
We've collected over 50,000 authentic exam questions and detailed explanations from around the globe. Log in now and get instant access to the answers!
Similar Questions
A cylindrical tank has a base radius of 5 cm and a height of 9 cm and is initially filled with water. The water flows out through a hole in the bottom of the tank at a rate of 5\( \sqrt[]{h} \)cm3/min, where h cm is the height of the water in the tank at time t. The time taken in minutes for the tank to empty is given by:
Question textThis is one of the problem sets that was part of the mock exam during COVID when the exam was fully online. There will be a problem set dedicated to differential equations on the real exam. However, that one will be hand-written. In general, to prepare for the differential equation part of the final exam, please make sure that you are familiar with the sample problems in the lecture notes and the applied class problem set.a) The differential equation with the initial condition y' = 2 x y, y(0) = 2has a solution of the form y(x) =What are c and d?Answer:c= Answer 1 Question 10[input]d= Answer 2 Question 10[input]b) A possible integrating factor for this differential equation y' + 3y/x = ex/x3is xc.What is c?Answer:c= Answer 3 Question 10[input]c) The differential equation y'' + 3 y' + 3 y = 6x+21has a particular solution of the form yp(x)=ax+b. What are a and b?Answer:a = Answer 4 Question 10[input]b = Answer 5 Question 10[input]
Question text 2Marks Let [math: y] be the solution to the initial value problem [math: x2dydx=ey and y(e)=1.]x^2\frac{dy}{dx}=e^{y}\ \text{ and }\ y(e)=1. Then the graph of [math: y] has an asymptote at [math: x=]Answer 5[input] and [math: y(1)=]Answer 6[input].Notes Report question issue Question 38 Notes
Consider the differential equation: . If the general solution is , which one of the following is the value of ?
More Practical Tools for Students Powered by AI Study Helper
Making Your Study Simpler
Join us and instantly unlock extensive past papers & exclusive solutions to get a head start on your studies!