Exponential Relations:

1. The half-life of a radioactive material is 5 hours. This means that only half of the previous amount of material remains after every 5 hour period Complete the table of values if the initial amount of material was 800 mg. Graph the relationship between time and the amount remaining. (Hint: For time start at 0 then use increments of 5 -the half life) Time (h) Amount Remaining (mg) b ) Create an equation to model your data. Define the variables and any restrictions on them. c) How much material remained after 30 hours? d) How long did it take for there to be less than 10% of the original left? e) Explain how you know this relationship is exponential. (give 2 reasons) f) When will there be no radioactive material left? Explain your answer.2. Mathville is experiencing a period of population growth. A new manufacturing sector and additional community complexes has people moving to the town. In 2000 the population was only 1000 people, but it has grown at a rate of 25% each year. a) Complete the table of values showing the population of Mathville for 12 years. Illustrate the population growth on a graph. year Population 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 b) Create an equation to model your data. Define the variables and any restrictions on them. c) What was the population in 2006? d) How long did it take for the population to reach 5000 people? e) Explain how you know this relationship is exponential. Give 2 reasons. f) Predict what the population will be in 2020. Will the population of Mathville continue to grow forever? Explain