A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material every week for 7 weeks and obtains the following data: Week Weight (in Grams) 0 1 2 3 69.4 100.0 88.3 75.9 4 5 59.1 51.8 6 45.5 (a) Using a graphing utility, draw a scatter diagram with week as the independent variable. (b) Using a graphing utility, build an exponential model from the data. (c) Express the function found in part (b) in the form A1t2 = A0 ekt. (d) Graph the exponential function found in part (b) or (c) on the scatter diagram. (e) From the result found in part (b), determine the half-life of the radioactive material. (f) How much radioactive material will be left after 50 weeks? (g) When will there be 20 grams of radioactive material?
S343 Section 2.5 Notes- Autonomous Equations and Population Dynamics 9-6-16 Autonomous equation- = where /independent variable does not appear explicitly o Separable; several uses as models for exponential/logistic growth Exponential Growth o Let = () be population at time ; rate of change of proportional to current value of = where = rate of growth/decline = 1 = 1 ∫ = ∫ ln = +
