7:41 PM Sat Mar 21 * 100% 12. Chemistry. Erbium-165 decays at a rate proportional to the amount present. a. A lab technician has a 4-mg sample of erbium-165, and 10.4 hr later, the sample has reduced to 2 mg. Write an equation that gives the amount, A(t), of erbium-165 present after t hours. b. After how long will only 10% of the original sample remain? 13. Population decay. The population of Cortez Breaks decreases at a rate proportional to the current size of the population. a. In 2012, the population was 5000; by 2018, the population was 2500. Write an equation that gives the population, P(t), of Cortez Breaks t years after 2012. b. After how long will the population of Cortez Breaks be only 30% of the 2012 population? 14. Population decay. The student population at Silver Bell College decreases at a rate proportional to the current size of the population. a. In 2010, the student population was 10,000; by 2017, the student population was 5000. Write an equation that gives the student population, P(t), of Silver Bell College after t years. b. After how long will the student population be only 40% of the 2010 population? In Exercises 150-220, find the half-life for each situation. 15. An element loses 12% of its mass every year. 16. A population of bacteria decreases by 5.75% per month. 17. A vehicle loses 0.8% of its value every month. 18. A city loses 3.9% of its population every year. 19. The value of a dollar decreases by 3% every year. 20. An element loses 1.75% of its mass every day. 21. An investment loses 1.9% of its value every week. 22. A motor home loses 0.5% of its value every week.