1. Answers to even-numbered HW problems Section 4.2 S-8 Yes, it shows exponential growth because x values are evenly spaced and ratios of successive y values are approximately equal. S-10No, the data are not exponential because g(t) = 38.30(.930 t ) Ex 4 The first data set is exponential: f(t) = 6.70(1.16 t ) The second data set is linear : g(t) = 1.73t + 5.80 Exponential because t values are evenly spaced and ratios of successive y values are equal. tf(t)t 06.70310.46 17.77412.13 29.02514.07 Table A tf(t)t 05.80310.99 17.53412.72 29.26514.45 Table B x0123 y2.67.823.470.2 x0246 y592143 tf(t)t 038.301216.04 428.651611.99 821.43208.97 Ex 2

2. Ex 14 a. b. Yearly growth factor is 1.02 c. Hourly wage in 1990 was $15.00 d. W = 15.00(1.02 t ) e. Yearly percentage raise was 2%. f. No, the salary only rose by about 29% for the decade Time t (t = years since 1990) Hourly Wage W 115.30 215.60 315.90 416.25 Since the ratios of successive wages are approximately equal, the data are exponential.

3. Uranium 239 (U 239 ) is an unstable isotope of uranium that decays rapidly. In order to determine the rate of decay, 10 grams were placed in a container, and the amount remaining was measured at 5-minute intervals and recorded in the table below. Time in minutes Grams remaining 010 58.63 107.45 156.43 205.55 1.Show that an exponential model would be appropriate for this data. 2.What is the decay factor per minute (nearest thousandth)? 3.Find an exponential model for the data. 4.What is the decay rate each minute? What does this number mean in practical terms? 5.Use functional notation to express the amount remaining after 13 minutes and then calculate that value. U Periodic Table of Elements

4. Uranium 239 (U 239 ) is an unstable isotope of uranium that decays rapidly. In order to determine the rate of decay, 10 grams were placed in a container, and the amount remaining was measured at 5-minute intervals and recorded in the table below. Time in minutes Grams remaining 010 58.63 107.45 156.43 205.55 1.Show that an exponential model would be appropriate for this data. Since the times are evenly spaced and the ratios (quotients) of successive amounts of uranium are approximately equal, an exponential model is appropriate. U Periodic Table of Elements

5. Uranium 239 (U 239 ) is an unstable isotope of uranium that decays rapidly. In order to determine the rate of decay, 10 grams were placed in a container, and the amount remaining was measured at 5-minute intervals and recorded in the table below. Time in minutes Grams remaining 010 58.63 107.45 156.43 205.55 1.Show that an exponential model would be appropriate for this data. 2.What is the decay factor per minute (nearest thousandth)? U Periodic Table of Elements

6. Uranium 239 (U 239 ) is an unstable isotope of uranium that decays rapidly. In order to determine the rate of decay, 10 grams were placed in a container, and the amount remaining was measured at 5-minute intervals and recorded in the table below. U Time in minutes Grams remaining 010 58.63 107.45 156.43 205.55 1.Show that an exponential model would be appropriate for this data. 2.What is the decay factor per minute (nearest thousandth)? 3.Find an exponential model for the data. G(t) = 10 where t = number of minutes and G(t) = the number of grams of uranium remaining. Periodic Table of Elements.971

7. G(t) = 10 Uranium 239 (U 239 ) is an unstable isotope of uranium that decays rapidly. In order to determine the rate of decay, 10 grams were placed in a container, and the amount remaining was measured at 5-minute intervals and recorded in the table below. Time in minutes Grams remaining 010 58.63 107.45 156.43 205.55 1.Show that an exponential model would be appropriate for this data. 2.What is the decay factor per minute (nearest thousandth)? 3.Find an exponential model for the data. 4.What is the decay rate each minute? What does this number mean in practical terms? 1 –.971 =.029 or 2.9%. The decay rate per minute is 2.9%. It means that 2.9% of the uranium is lost every minute. U Periodic Table of Elements.971

8. Uranium 239 (U 239 ) is an unstable isotope of uranium that decays rapidly. In order to determine the rate of decay, 10 grams were placed in a container, and the amount remaining was measured at 5-minute intervals and recorded in the table below. Time in minutes Grams remaining 010 58.63 107.45 156.43 205.55 1.Show that an exponential model would be appropriate for this data. 2.What is the decay factor per minute (nearest thousandth)? 3.Find an exponential model for the data. 4.What is the decay rate each minute? What does this number mean in practical terms? 5.Use functional notation to express the amount remaining after 13 minutes and then calculate that value. G(13) = There are approximately 6.82 grams of uranium remaining after 13 minutes. U Periodic Table of Elements 2.9%.971 G(t) = 10

9. Uranium 239 (U 239 ) is an unstable isotope of uranium that decays rapidly. In order to determine the rate of decay, 10 grams were placed in a container, and the amount remaining was measured at 5-minute intervals and recorded in the table below. Time in minutes Grams remaining 010 58.63 107.45 156.43 205.55 1.Show that an exponential model would be appropriate for this data. 2.What is the decay factor per minute (nearest thousandth)? 3.Find an exponential model for the data. 4.What is the decay rate each minute? What does this number mean in practical terms? 5.Use functional notation to express the amount remaining after 13 minutes and then calculate that value. 6.The half-life of a radioactive element is the time it takes for the mass to decay by half. Use the graphing calculator to find the half-life of U 239 to the nearest hundredth of a minute. U Periodic Table of Elements 2.9%.971 G(t) = 10 G(13) = 6.82g

10. Uranium 239 (U 239 ) is an unstable isotope of uranium that decays rapidly. In order to determine the rate of decay, 10 grams were placed in a container, and the amount remaining was measured at 5-minute intervals and recorded in the table below. Time in minutes Grams remaining 010 58.63 107.45 156.43 205.55 6. The half-life of a radioactive element is the time it takes for the mass to decay by half. Use the graphing calculator to find the half-life of U 239 to the nearest hundredth of a minute. U Periodic Table of Elements 23.55 minutes

11. Planet Average Distance from the Sun (in millions of km) Time to Make Complete Orbit (in days) Mercury57.9 88 Venus108.2 225 Earth149.6 365 Mars228.0 687 Jupiter778.6 4333 Saturn1427.4 10760 Uranus2838.2 30686 Neptune4497.8 60191 Pluto5913.5 90739 Shown below are the average distances from the sun (in millions of kms) of the planets in the solar system. Just a few years ago, astronomers removed Pluto from the list. Graph the data, representing the planets by the numbers 1 – 8 (based on their positions in the solar system). = 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8

12. Planet Average Distance from the Sun (in millions of km) Time to Make Complete Orbit (in days) Mercury57.988 Venus108.2225 Earth149.6365 Mars228.0687 Jupiter778.64333 Saturn1427.410760 Uranus2838.230686 Neptune4497.860191 Pluto5913.590739

13. Planet Average Distance from the Sun (in millions of km) Time to Make Complete Orbit (in days) Mercury57.988 Venus108.2225 Earth149.6365 Mars228.0687 Jupiter778.64333 Saturn1427.410760 Uranus2838.230686 Neptune4497.860191 Pluto5913.590739 where D = average distance from the sun and p = position in solar system. Based on the exponential regression model, does Pluto qualify as a planet?

14. Homework: Read Section 4.3 Page 350-351 # S-2, S-3, S-5, S-10, S-11 Pages 351-357 # 1, 5, 6, 19 a,b,c,d