Bacteria grow in a culture at a rate proportional to the amount present. In Show more Supplementary Problems 1)Bacteria grow in a culture at a rate proportional to the amount present. Initially 300 strands of the bacteria are in the culture and after two hours that number has grown by 20 percent.
Bacteria grow in a culture at a rate proportional to the amount present. In Show more Supplementary Problems 1)Bacteria grow in a culture at a rate proportional to the amount present. Initially 300 strands of the bacteria are in the culture and after two hours that number has grown by 20 percent.
Find (a) an expression for the approximate number of strands in the culture at any time t and (b) the time needed for the bacteria to double its initial size. 2)A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there are 100 milligrams of the material present and if after two years it is observed that 5 percent of the original mass has decayed find (a) an expression for the mass at any time t and (b) the time necessary for 10 percent of the original mass to have decayed. 3)A body at a temperature of 50 F is placed in an oven whose temperature is kept at 150 F. If after 10 minutes the temperature of the body is 75 F find the time required for the body to reach a temperature of 100 F. 4)A ball is propelled straight up with an initial velocity of 250 ft/sec in a vacuum with no air resistance. How high will it go? 5)A tank initially holds 80 gal of a brine solution containing ^lb of salt per gallon. At t = 0 another brine solution con- taining 1 Ib of salt per gallon is poured into the tank at the rate of 4 gal/min while the well-stirred mixture leaves the tank at the rate of 8 gal/min. Find the amount of salt in the tank when the tank contains exactly 40 gal of solution. Show less
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