chapter4

# 7 it was estimated that the earths human population

This preview shows pages 35–40. Sign up to view the full content.

7. It was estimated that the earth’s human population in 1961 was 3,060,000,000. Assuming the population increases at the rate of 2 112

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
percent, find the earth’s population in 1996 using model of population growth (1.8). Check this number with the actual population of the earth available from authentic sources. 113
Radio-Active Decay and Carbon Dating 8. A breeder reactor converts relatively stable uranium 238 into the isotope plutonium 239. After 30 years it is determined that 0.022% of the initial amount N 0 of plutonium has disintegrated. Find the half-life of this isotope if the rate of disintegration in proportional to the amount remaining. 9. The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 4 hours. If 1 gram of lead is present initially, how long will it take for 80% of the lead to decay? 10. Solve the model obtained in Exercise 32 of chapter 1. 11. In the 1950 excavation at Nippur, a city of Babylonia, charcoal from a roof beam gave a count of 4.09 dis/min/g. Living wood gave 6.68 disintegrations. Assuming that this charcoal was formed during the time of Hammurabi’s reign, find an estimate for the likely time of Hammurabi’s succession. Mixture of Two Salt Solutions 12. A tank with a capacity of 600 litres initially contains 200 litres of pure water. A salt solution containing 3 Kg of salt per litre is allowed to run into the tank at a rate of 16 lit/min, and the mixture is then removed at a rate of 12 lit/min. Find the expression for the number of Kilograms of salt in the tank at any time t. 114

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
13. A large tank is filled with 600 liters of pure water. Brine containing 2 Kg of salt per litre is pumped into the tank at a rate of 5 litre/min. The well-mixed solution is pumped out at the same rate. Find the number P(t) of kilograms of salt in the tank at time t. What is the concentration of the solution in the tank at t=10 min? 14. A 250-litre tank contains 100 litres of pure water. Brine containing 4 kg of salt per litre flows into the tank at 5 lit/hr. If the well-stirred mixture flows out at 3 lit/hr, find the concentration of salt in the tank at the instant it is filled to the top. Series circuit 15. A series RL circuit has a resistance 20 ohms, and an inductance of 1 henry, and an impressed voltage of 12 volts. Find the current i(t) if the initial current is zero. 16. An electromotive force 120, 0 t 20 E(t)= 0 , t > 20 is applied to an LR series circuit in which the inductance is 20 henries and the resistance is 2 ohms. Find the current i(t) if i(0)=0 Survivability with AIDS 17. Find survival fraction S(t) with aids after 2 years by applying model (1.31). 115
Draining a Tank 18. A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. Let us assume that the height of the tank is 10 ft. high and has radius 2 ft. and circular hole has radius ½ inches. If the tank is initially full, how long it will take to empty? Economics and Finance 19. What rate of interest payable annually is equivalent to 6% continuously compounded?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern