1. A body at a temperature of 50°F is placed outdoors where the temperature is 100°F. If after 5 minutes the temperature of the body is 60°F, find (a) how long it will take the body temperature to reach a temperature of 75°F and (b) the temperature of the body after 20 minutes. 2. A body at an unknown temperature is placed in a room which is held at a constant temperature of 30°F. If after 10 minutes the temperature of the body is 0°F and 20 minutes the temperature is 15°F, find the unknown initial temperature. 3. If the temperature of the air is 300K and the substance cools from 360K to 330K in 10 minutes, find when the temperature of the substance will be 310K. 4. When a cake is removed from an oven, its temperature is measured at 320°F. Three minutes later its temperature is 210°F. How long will it take for the cake to cool off to a room temperature of 80°F? 5. The population of a certain country is known to increase at a rate proportional to the number of people presently living in the country. If after two years the population has doubled, and after three years the population is 20,000, find the number of people initially living in the country. 6. In a certain culture of bacteria, the rate of increase is proportional to the number present. (a) If it is found that the number doubles in 6 hrs, how many may be expected at the end of 18 hrs? (b) If there are 10² at the end of 4 hrs, and 8 · 102 at the end of 8 hrs, how many were there in the beginning? 7. A tank initially contains 60 gallons of brine in which there is dissolved 8 Ibs. of salt. Brine containing 2 Ibs. of dissolved salt per gallon flows into the tank at the rate of 5 gal/min. The mixture is kept uniform by stirring, and the stirred mixture simultaneously flows out at the slower rate of 3 gal/min. How much salt is in the tank at any time t>0? 8. A 120-gallon tank initially contains 80 Ibs. of salt dissolve in 90 gal of water. Brine containing 2lbs/gal of salt flows into the tank at the rate of 5 gal/min, and the mixture flows out of the tank at the rate of 4 gal/min. If the tank is full after 40 minutes, how much salt does the tank contain? 9. A large tank contains 100 gallons of brine in which 10 Ibs. of salt is dissolved. Brine containing 0.2 Ibs. of salt to the gallon runs into the tank at the rate of 6 gal/min. The mixture, kept uniform by stirring, runs out of the tank at the rate of 4 gal/min. Find the amount of salt in the solution in the tank at the end of t min.