Applications of Derivative (Exponential Growth and Decay)

MUFY MATHEMATICS UNIT 1 - STUDY AREA 3 The population of Skeviland can be modeled by P= 1.8e .", where t is the time in 3. years since January 1990 and P is the population in millions. What was the population of Skeviland in 1990? (a) In what year will the population have doubled? At what rate will the population be growing in the year 2001? (c) A sample of Polonium-210 has a mass of 300 grams and half-life of 140 days. Its 4. mass after t days can be modeled by P = Pet" where P. is the initial mass. (a) Find the value of Po and k. (b Find the mass that remains after 20 days. Find the rate of decrease in the mass of the sample after 20 days. (d) How long will the sample take to decay to a mass of 100 grams and what will be its rate of decrease at this time? 5. The decay of an isotope can be modeled by I =100e-" where its mass I is measured in grams and t is measured in minutes. Its mass after 2 minutes is 80 grams. (a) Find the mass in grams of the isotope after t minutes. (b) minutes . Find the average rate of decrease in the mass of the isotope over the first 10 (C) Find the rate of decay after 2 minutes. (d) amount. Find the rate of decrease of the isotope when the mass is half its initial