MBF3C Date: Investigating Exponential Relations Practice 1. Determine if each relation is exponential. a) Ratio of b Ratio of C Ratio of Successive Successive y Successive y-values y-values y-values 2 3 1 4 2 2 16 3 3 27 8 8 4 81 4 256 5 10 5 243 5 625 6 12 6 729 6 1296 Exponential? Exponential? Exponential? 2. Which of the following graphs could represent an exponential relation? Circle Yes or No. a ) Yes No b ) Yes No c ) Yes No d) Yes No 3. A car purchased for $38 000 depreciates by 30% each year. This can be represented by the relation V = 38 000(0.70) , where I is the value of the car in dollars and t is the time in years. Find the value of the car after each period. a) 1 year b) 3 years c) 5 years d) 9 yearsDate: 4. The graph shows the temperature of a pot of water over time. y Heating Water a) Describe the shape of the graph for the first 20 minutes. -400 90 80. b) Describe the shape of the graph after the first 20 minutes. 60 c) What is the approximate temperature after 15 minutes? Temperatu 30 20. d) Suggest reasons for the change in the shape of the graph. 10 20 30 40 X Time (min) 5. Ms. Gabrielse's math students wanted to know how much homework was expected in her course. She suggested they spend 2 seconds on homework on the first night, and then double the time spent on homework every night (not including weekends) throughout the course. a) How much homework does Ms. Gabrielse Day Time in Time in Time in expect at the end of the first week of classes? # Seconds Minutes Hours (x) ( 2 * ) (sec : 60) (min : 60) 1 2 0.0333 0.00056 N 4 0.0667 0.00111 b) How much homework does Ms. Gabrielse 3 8 0.1333 0.00222 expect at the end of the first week of classes 4 at the end of the first month of classes? 5 (Assume there are 20 school days in a month) 6 7 8 c) Estimate when the time spent on homework 10 is one hour. 1 1 12 13 d) Estimate when the time spent on homework 14 is one day. 15 16 17 18 19 20