1. Radium has a half-life of 1600 years. How much radium will be left from a 1000-gram sample after 1600 years?

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1 The Radioactive Deca Eperiment ACTIVITY 7 Learning Targets: Given a verbal description of a function, make a table and a graph of the function. Graph a function and identif and interpret ke features of the graph. SUGGESTED LEARNING STRATEGIES: Discussion Groups, Look for a Pattern, Construct an Argument, Paraphrasing, Marking the Tet, Think-Pair-Share In the late nineteenth centur, the scientist Marie Curie performed eperiments that led to the discover of radioactive substances. A radioactive substance is a substance that gives off radiation as it decas. Scientists describe the rate at which a radioactive substance decas as its half-life. The half-life of a substance is the amount of time it takes for one-half of the substance to deca.. Radium has a half-life of 600 ears. How much radium will be left from a 000-gram sample after 600 ears? CONNECT TO SCIENCE How much is half a life? The half-life of a radioactive substance can be as little as seconds for Polonium- and as much as. billion ears for Uranium-8.. How much radium will be left after another 600 ears?. Suppose a radioactive substance has a half-life of second and ou begin with a sample of grams. Complete the table of values. 0 College Board. All rights reserved. Time (seconds) Amount Remaining (grams) 0 Activit 7 Graphs of Functions 0

2 ACTIVITY 7 The Radioactive Deca Eperiment. Graph the data from the table on the grid below. Amount Remaining (grams) Time (seconds). Make use of structure. Will the amount of the substance that remains ever reach 0? Eplain. 6. What are the reasonable domain and range of the function represented in the graph? Eplain. 7. What is the -intercept and what does it represent? 8. Identif the absolute maimum and minimum of the function represented in the graph, and tell what the represent in the contet. 0 College Board. All rights reserved. 06 Unit Functions

3 The Radioactive Deca Eperiment ACTIVITY 7 The function that describes the substance s deca is f. The graph of this function when it does not model a real-world situation is shown below. ( )= ( ) 0 9. What are the domain and range of the function? 0. How is this graph different from our graph in Item? 0 College Board. All rights reserved.. How do the values of change as the values of increase?. How do the values of change as the values of decrease?. Identif the absolute maimum and absolute minimum of the function. Activit 7 Graphs of Functions 07

4 ACTIVITY 7 The Radioactive Deca Eperiment Check Your Understanding. A scientist has g grams of a radioactive substance. Write an epression that shows the amount of the substance that remains after one half-life.. Critique the reasoning of others. Dlan looked at the function f and said, This function is alwas greater than 0, so 0 is the absolute minimum. Eplain wh Dlan is incorrect. ( )= ( ) Suppose the value of our new car is reduced b half ever ear that ou own it. You paid $0,000 for our new car. 6. Describe how this situation is similar to the half-life of a radioactive substance. 7. Cop and complete the table below. Time (ears) Value ($) 0 0, Make sense of problems. For insurance purposes, a vehicle is considered scrap when its value falls below $00. After how man ears will our new car be considered scrap? 0 College Board. All rights reserved. 08 Unit Functions

5 Eperiment Eperiences ACTIVITY 7 0 College Board. All rights reserved. Write our answers on notebook paper. Show our work. Lesson 7- A weight of ounces stretches a spring 0 inches. A weight of ounces stretches the same spring 6 inches. Use this information to answer Items.. How man inches does the spring stretch per ounce of additional weight? A. inch B. inches C. inches D. 0 inches. Write an equation to describe the relationship between the distance d that the spring stretches and the weight w that is attached to it.. How much will the spring stretch for a weight of 9 ounces?. The spring is stretched inches. How man ounces is the weight that is attached to it? A spring stretches. inches for each ounce of weight. Use this information for Items 7.. Determine a function that represents this situation. 6. If ou were to graph the function represented b this situation, what would be the reasonable domain? Eplain. 7. Which of the following data points would not lie on the graph representing this function? A. (0, 0) B. (,.) C. (., ) D. (0, ) Lesson 7- Suppose that the height of an object after seconds is given b f ( ) = 00, as shown in the graph below Use the function or the graph for Items What is the reasonable domain of the function? 9. What is the reasonable range of the function? 0. Identif the -intercept of the function.. What does the -intercept represent?. Identif the -intercept of the function.. What does the -intercept represent?. Loni sas that because of the negative sign in front of, the reasonable domain for this function is onl negative values. Is her reasoning correct? Eplain. Activit 7 Graphs of Functions 09

6 ACTIVITY 7 Eperiment Eperiences Lesson 7-. The half-life of a radioactive substance is hour. If ou begin with 00 ounces of the substance, how man hours does it take for. ounces to remain? The graph below represents a radioactive deca situation. Use this graph for Items 6 8. Amount Remaining (grams) Time (ears) 6. What is the original amount of the radioactive substance? Eplain how ou know. 7. What are the reasonable domain and range? 8. Identif the absolute maimum and absolute minimum values of the function. What do these values represent? Barr has a piece of paper whose area is 0 square inches. He cuts the paper in half and discards one of the pieces. He repeats this procedure several times. Use this information for Items Cop and complete the table below to show the area of the remaining piece of paper after cuts. Number of Cuts, Area of Remaining Piece, Describe how this situation is similar to the half-life of a radioactive substance.. If ou were to graph the points from the table, would ou connect the points? Eplain.. Describe how the reasonable domain in this situation is different from the reasonable domain in a radioactive deca situation.. Identif the -intercept. What does it represent?. Identif the absolute maimum value. What does it represent? MATHEMATICAL PRACTICES Construct Viable Arguments and Critique the Reasoning of Others. Maude receives $00 for her birthda. I am going to spend half of m birthda mone each da until none is left, she decides. Is it reasonable for her to believe that she will eventuall spend all of the mone? Justif our answer. 0 College Board. All rights reserved. 0 Unit Functions

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