Oil reserves decrease at a constant proportional rate, k > 0, so that dN/dt = -kN where
Question:
Oil reserves decrease at a constant proportional rate, k > 0, so that
dN/dt = -kN
where N denotes the number of barrels of oil remaining in t years’ time.
(a) Write down an expression for N(t) when current oil reserves are A barrels.
(b) Show that the time taken for oil reserves to fall to half their current levels is (ln 2)/k.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 47% (17 reviews)
a N Aer ...View the full answer
Answered By
Muhammad Salman Alvi
Well, I am a student of Electrical Engineeing from Information Technology University of Punjab. Just getting into my final year. I have always been good at doing Mathematics, Physics, hardware and technical subjects. Teaching profession requires a alot of responsibilities and challenges.
My teaching experience started as an home tutor a year ago. When I started teaching mathematics and physic subjects to an O Level student. He was about 14 years old. His name was Ibrahim and I used to teach him for about 2 hours daily. Teaching him required a lot of patience but I had to be polite with him. I used to give him a 5 min break after 1 hour session. He was quite weak in basic maths and calculation. He used to do quite a lot of mistakes in his homework which I gave him weekly. So I decided to teach him basics from scratch. He used to say that he got the concept even if he didn't. So I had to ask him again and again. I worked on his basics for a month and after that I started taking a weekly test sesions. After few months he started to improve gradually. Now after teaching him for about a year I can proudly say that he has improved alot. The most important thing was he managed to communicate all the difficullties he was facing. He was quite capable and patient. I had a sincere desire to help him reach to its full potential. So I managed to do that. We had a very good honest relationship of a student and a teacher. I loved teaching him as a tutor. Now having an experience of one year teaching I can read students quite well. I look forward to work as an online tutor who could help students in solving their all sort of difficulties, problems and queries.
4.90+
29+ Reviews
43+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Water in an open bowl evaporates at a rate proportional to the area of the surface of the water. (This means that the rate of decrease of the volume is proportional to the area of the surface.) Show...
-
Suppose that r(t) = r 0 e -kt , with k > 0, is the rate at which a nation extracts oil, where r 0 = 10 7 barrels/yr is the current rate of extraction. Suppose also that the estimate of the total oil...
-
A cross-sectional study was carried out to assess the relationship of alcohol and smoking to blood pressure in 2,500 men ages 20 years or older in four North American population groups, each group...
-
To anticipate subsequent chapters where more complicated renewable resource models are introduced, consider a slight modification of the two-period depletable resource model. Suppose a biological...
-
An ideal Rankine power cycle shown in Fig. 8.32 has a boiler that produces steam at 600 psia and 900°F with a mass flux of 18 lbm/s. The steam leaving the turbine has a pressure of 10 psia....
-
Reba, a calendar year taxpayer, owns an office building that she uses in her business. The building is involuntarily converted on November 15, 2021. On January 5, 2022, Reba receives enough proceeds...
-
How many forms of main() are there?
-
Lenni Clothing Co. manufactures clothing in a small manufacturing facility. Manufacturing has 25 employees. Each employee presently provides 40 hours of productive labor per week. Information about a...
-
Defend the following statement: Data and database administration are even more important in the decentralized IS environment than in the centralized one
-
Tamar owns a condominium near Cocoa Beach in Florida. In 2022, she incurs the following expenses in connection with her condo: Insurance Advertising expense Mortgage interest Property taxes Repairs &...
-
Consider the market model Q S = 3P - 1 Q D = -2P + 9 dP/dt = 0.5(Q D - Q S ) Find expressions for P(t), Q S (t) and Q D (t) when P(0) = 1. Is this system stable or unstable?
-
Find the equilibrium price and quantity given the following static supply and demand equations: Q S = 6P 10 Q D = 4P + 45 The equations for the corresponding dynamic model are: Find an expression...
-
Consider subsonic Rayleigh flow that is accelerated to sonic velocity (Ma = 1) at the duct exit by heating. If the fluid continues to be heated, will the flow at duct exit be supersonic, subsonic, or...
-
Use Monte Carlo Method to estimate the following integral. 1 L -1 (x + sin (x)) dx Write Python code with n = 10^6. Use the random seed 0. Question 2. Use composition approach to simulate the...
-
The column space of each matrix A and B below determines a plane in R. We will find a non-zero vector in the intersection of the two planes, i.e., a vector v in C(A) nC(B). 1 2 13 B 6 3 5 1 2 We want...
-
Economic and accounting profits a) (10 marks). ( i) What are economic profits and how do they differ from accounting profits? (ii) If accounting profits are positive then does this imply that...
-
Harvick mistakenly failed to use the correct figures in preparing a tax return for Menard's company. The IRS saw the inaccuracies, and Menard was ordered to pay $500,000 in additional tax. What...
-
John has three years to save up $50,000 and finds a credit union that will pay 6% p.a. compounding monthly. How much does he need to deposit today? 2) John finds a bank that offers an effective...
-
Several volcanoes have been observed erupting on the surface of Jupiter's closest Galilean moon, Io. Suppose that material ejected from one of these volcanoes reaches a height of 5.00 km after being...
-
Annual dividends of ATTA Corp grew from $0.96 in 2005 to $1.76 in 2017. What was the annual growth rate?
-
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. If n and r are positive integers and 1 < r < n, then n C r < n P r .
-
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. If n and r are positive integers and 1 < r < n, then n C r < n P r .
-
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample. If n and r are positive integers and 1 < r < n, then n C r < n P r .
-
Project: Design a coherent and complete children's dental health promotion program. You can focus on either one key element of dental health or the full program. Make sure all your materials work...
-
1) h C b 2) S S b = 9.17 mm a = 4.4 mm c = 9.8 mm h = 4.1 mm Area: Perimeter: Type: s = 5.5 yds h = 4.8 yds Area: Perimeter: Type: 5) 4) b a h C S S S h S a = 5.81 cm b = 8.48 cm c = 9.3 cm h = 5.2...
-
Would love some support on this I cannot find all 20 errors! The question: Dear Colleague, Earlier today I built my third website using HTML5. Based on what we had learned in Exercises 1 through 9, I...
Study smarter with the SolutionInn App