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MBF3C: Mathematics of Personal Finance Day 4: Investigating Exponential Relationships Date: ____________ Unit 6: Exponents Investigating Exponential Relationships The temperature data collected by a temperature probe has been recorded in the following table. a) Calculate the 1st Differences (y2 – y1) b) Calculate the 2nd Differences (1st Diff2 – 1st Diff1) c) Calculate the Ratio of Successive y-values (y2 ÷ y1) d) Plot the (x, y) coordinates and draw the graph. x y 0 2 1 6 2 18 3 54 4 162 5 486 1st 2nd Ratio of Successive Differences Differences y-values In an ________________________ relation, for equal steps of x, neither the 1st or 2nd differences are __________________, but the _____________of consecutive _______________ are constant. The graph ________________ rapidly as you move to the right on the x-axis, and approaches a __________________ line. This is an example of exponential ____________________. TERMINOLOGY Exponential Growth: ____________________ growth represented by an exponential relation and a graph with a rapidly ______________________ ________________ curve Exponential Decay: ____________________ decay represented by an exponential relation and a graph with a rapidly ______________________ __________________ curve Page 1 of 2 MBF3C: Mathematics of Personal Finance Day 4: Investigating Exponential Relationships Date: ____________ Unit 6: Exponents An EXPONENTIAL FUNCTION is a function with a _________________ in the exponent. y 2 Some examples would be y 10 x x 2 y 3 y ax x 1. Sketch the graphs of y 2x and y 3x on the same axes x y 2x x -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 y 3x a) Comparing to the general exponential function y a x , is a 1 or is 0 a 1 ? _________ . b) What is the y-intercept ? ________________ . Is there an x-intercept ? ______ . c) Are the functions increasing or decreasing?_____________________ . x x 1 1 2. Sketch the graphs of y and y on the same axes 2 3 x 1 y 2 x x -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 1 y 3 x a) Comparing to the general exponential function y a x , is a 1 or is 0 a 1 ? _________ . b) What is the y-intercept ? ________________ . Is there an x-intercept ? ______ . c) Are the functions increasing or decreasing?_____________________ . Page 2 of 2