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- Cesium-137 has a half-life of about 30 years. If we begin with 200 mg of cesium-137, will it take more or less than 230 years until only 1 milligram remains?The population of Normal, Illinois grows proportionally to its population at time t. At an initial population of 2100, it grows at a rate of 8% over 10 years. What is the value of the proportionality constant?To find the revenue function, we integrate the marginal revenue function. In this case we can use the Exponential Formula, eu · u' dx = eu + C. R(x) = 8e0.01x dx
- Rank the functions x100, ln x10, xx, and 10x in order of increasinggrowth rates as x→ ∞.Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1) where x=0 corresponds to year 1990. A) How many pounds of Aluminum were shipped in 2004 B) Assuming the continued accuracy of the model when will aluminum shipments reach 247,400,000,000 pounds.An oil tanker is leaking oil at a rate ofL ′ ( x ) = x e ^(− x/2)barrels per hour, where x is the time in hours after the tanker has hit a hidden rock (at x = 0). How many barrels will the ship leak on the first day?
- Total net shipments of aluminum (in billions of pounds) are approximated by g(x) = 16.2 + 2.86 In(x + 1) where x=0 corresponds to year 1990 a) How many pounds of aluminum were sipped in 2004? b) Assuming the continued accuracy of the model, when will aluminum shipments reach 27,400,000,000 pounds?A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a concentration of 0.5 kg per liter, is allowed to run into the tank at the rate of 3 liters a minute. Brine run out of the tank at the rate of 2 liters a minute. The instantaneous concentration in the tank is kept uniform by stirring. How much salt is in the tank at the end of one hour?One model for the way diseases die out when properly treated assumes that the rate dy/dt at which the number of infected people changes is proportional to the number y. The number of people cured is proportional to the number y that are infected with the disease. Suppose that in the course of any given year, the number of cases of a disease is reduced by 20%. If there are 10,000 cases today, how many years will it take to reduce the number to 1000?