Algebra II Assignment #______ Apps of Exponents Name: Date: Periods: Setup an exponential function to represent the information when not given an equation. Then answer the questions using your equation. 1. The Wienfly has a half-life of 2.5 hours. Suppose a sample contains 50 mg of Wienfly at 3 PM. a. Write an equation that models the amount y of Wienfly present in the sample at x minutes after 3 PM. b. Find the amount of Wienfly present at 8 PM. c. Find the time, to the nearest minute, when Wienfly has the amount of 278.95 mg. 2. The Franklins inherited $35000, which they want to invest for their daughter’s college education. Marlee, their daughter, is currently 8 years old in 2012. a. They invest it in long-term futures which earn 8.25% annual interest that is compounded monthly. If their daughter goes to college at age 18, how much money will they have for her education? b. On average the cost of 1 year at a liberal arts school has an annual increase rate of 9.4%. If the poll was taken in 2012 and found the average cost of 1 year of college is $28,000, what will the average cost be in 2022? c. Will the Franklins have enough money, not including scholarships, for their daughter to go to college? 3. Given the function f(x) = 20(0.90)x, where f(x) is the number of fish in Jason’s fish tank and x is the number of days since Jason set up the tank. a. How many fish did Jason have to start? b. What is happening to Jason’s fish? 4. MacArthur High School is holding a math contest. Each week, students are given math problems to solve. At the end of the week, only the top half of participants is invited to continue with the contest. If 200 students initially enroll to participate in the contest, the equation N(t) = 200(0.5)t can be used to determine the number of students, N(t), participating in the contest after t weeks. This will continue until there is only one student left, who will be declared the winner. a. When will there be only 25% of the original 200 students remaining? b. How many participants will be left after 3 weeks? 5. A used car purchased in July 2005 for $11,900. If the car depreciates 13% of its value each year, what is the value of the car to the nearest hundred dollars, in July 2011? 6. Carbon-14 is a radioactive isotope that scientists use to help them determine the age of various objects. It decays according the function A(t) = A0(0.999879)t, where A(t) is the amount of carbon-14 present in an object. A0 is the initial amount of carbon-14 and t is the time in years. If scientists found an object containing 30 grams of carbon-14, and they knew that the object originally contained 100 grams, how old is the object? Round your answer to the nearest year. 7. Sally, Jesse, and Raphael each have contributed $50 to a savings account that compounds yearly at a rate of 4%. a. How much money will they have after 20 years? b. When does the money triple? 8. Tyler invested $1000 in Kids Should Not Have Fun Toy Co. His investment decayed by 30%. a. What will his investment be worth in 2.5 years? b. After how many years will his investment be $150? 9. In 1950, the population of Vienke, Germany was 10,000 people. If the population has doubled every ten years since that time, the population growth can be represented by the function Pc = P0(2)x, where Pc is the current population, P0 is the initial population and x is the time in years. Find the population of the city in: a. 1960 b. 2000 10. Write an exponential equation, using the table of values, round all values to the nearest hundredth. a. Is the equation growth or decay? b. What does the correlation coefficient tell you about the data? x -5 -2 3 4 8 11 y 0.1517 0.2568 0.7 0.89 1.6230 3.5894 11. The accompanying table shows the average paycheck for Rex since 1984. Years 1984 1985 1986 1987 1988 1989 1990 Average 290 320 400 495 600 700 820 Paycheck 1991 1000 1992 1250 a. Write an exponential equation with the coefficients rounded to the nearest hundredth. b. What will the salary be for the year 2025? c. During what year will Rex’s salary be $2850?