7 it was estimated that the earths human population

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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
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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
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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
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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
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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?
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