7:10 AM Fri Jul 22 . . . 2% c ) d) 6. Jeff is purchasing a new vehicle for $35 000. It is known that the vehicle will depreciate by 20% of its current value every year. a) Write an equation that relates the depreciated value of the vehicle, , to the age of the vehicle, t, in years. b) Use the equation to determine the value of the vehicle 2 years after it is purchased. c) Approximately how long will it take the vehicle to depreciate to $3000? Initial Amount: Growth Rate: Period: Time: a b) c) Page 7. Cobalt-60, which has a half-life of 5.3 years, is used in medical radiology. A sample of 60 mg of the material is present today. a) Write an equation to relate the amount of cobalt-60 remaining and the number of half-life periods. b) What amount will be present in 10.6 years? c) Approximately how many years will it take for the amount of cobalt-60 to decay to 12.5% of its initial amount? Initial Amount: Growth Rate: Period: Time: a) b) C) 8. Buket wants to invest some money in an account that pays 3.5% annual interest, compounded yearly. She wants to have an accumulated amount of $600 at the end of 4 years. a) Identify the values of A, i, and n to be used in the formula P = A(1 + 1) . b) Determine how much Buket needs to invest today in order for her to reach her goal in 4 years. c) How much less would she need to invest if the financial institution were to offer her 4% annual interest? Show all work. Initial Amount Growth Rate: Period: Time: a) b ) C DID V7:10 AM Fri Jul 22 . . . 2% 4 TO O + Part B: Solving the Problem In this section, you are going to use the characteristics of exponential functions to find the answer. For each question, answer the question giving the clues that you used in determining your answer. You will be given five marks - four marks for your correct clues and one mark for the correct answer. 4. A colony of ants starts with an initial population of 50 and doubles every week for 2 months. a) Create a table of values for weeks 0 to 8 for the population of the colony. b) Graph the data from your table of values. c) Is the relationship between the ant population and the number of weeks exponential? Explain. d) Model the information using an equation. Initial Amount: Growth Rate: Period: Time a ) b) C) d) Page 2 5. An initial investment of $4000 earns interest at 4% per year, compounded annually. a) Create a table of values for the first 10 years of the investment. b) Graph the data from your table of values. c) Is the relationship between the time and the amount of the investment exponential? Explain. d) Write an equation to represent the data Initial Amount: Growth Rate: Period: Time: b ) O IN V C d) 6. Jeff is purchasing a new vehicle for $35 000. It is known that the vehicle will depreciate by 20% of its current7:11 AM Fri Jul 22 . . . 2% O + Page 4 9. When interest is compounded semi-annually, the formula used to find the amount of an investment is P ( 1+ 2 )" , where A represents the amount, P represents the principal invested, i represents the annual interest rate, as a decimal, and n represents the number of years of the investment a) Use the formula to determine the amount that each investment would be worth. ) $5000 at an annual rate of 4%, compounded semi-annually, for 10 years ii) $4000 at an annual rate of 5%, compounded semi-annually, for 20 years b) If interest is compounded quarterly, the formula becomes A = P|1+ |. Use the formula to determine the amount that the investments from part a) would be worth if they were compounded quarterly. c) Explain the difference in the answers for parts a) and b). Initial Amount: Growth Rate: Period: Time: a) b ) c) 10. A radioactive sample with an initial mass of 72 mg has a half-life of 10 days. a) Write a function to relate the amount remaining, A, in milligrams, to the time, t, in days. b) What amount of radioactive sample will remain after 20 days? c) What amount of radioactive sample was there 30 days ago? d) How long, to the nearest day, will it take for there to be 0.07 mg of the initial sample remainin Initial Amount: Growth Rate: Period: Time a b) C d) V Page 57:10 AM Fri Jul 22 . . . 2% TOD O For each question, answer the question giving the clues that you used in determining your answer. You will be given two marks - one mark for your correct clues and one mark for the correct answer. 1. A radioactive sample with an initial mass of 35 mg has a half-life of 3 days. Which of the following equations models the exponential decay for time, t, in days? Initial Amount: Growth Rate: Period: Time Equation: A = 35(2) 3 C. A = 354 b. A = 354 d. A = 35 (2) 7 2. A bacterial colony with an initial population of 50 doubles every 5 h. Which of the following equations models the exponential growth for time, t, in hours? Initial Amount: Growth Rate: Period: Time: Equation: a. A = 50(2) 7 "A = 504 b. A = 50- d. A = 50(2 ) 3 Page 1 3. Which equation can be used to model the given information? Year (x) Population (v) 0 700 728 757 787 820 > 854 Initial Amount: Growth Rate: Period: 0 1 - Time Equation: V a. y = 700(1.4)* C. y = 700(1.04) *-1 b. y = 700(1.04)* d. y = 700(1.4) *-1