Linear and exponential functions

“The greatest shortcoming of the human race is our inability to understand the exponential function.”  Albert Bartlett

Learning objectives

  •  Recognize and model linear functions in graphical, numerical, and algebraic form
    •  f(x) = m x + b where m = (f(x_2)-f(x_1))/(x_2-x_1)
    • \Delta f = (slope) \cdot (\Delta x)
  • Recognize exponential functions in graphical, numerical, or algebraic form
  • Model exponential data in each of the forms a 2^{\pm t/T}, a e^{kt} using half life or doubling time T, or growth rate k = (\ln f(t_2) - \ln f(t_1))/(t_2-t_1)
  • Understand why we think in terms of families of functions
  • Distinguish parameters from independent variables
  • Use R to define functions and make graphs

Before class

  • Read Hughes-Hallett 1.1 – 1.3, 1.5 – 1.7 (but skip p. 55).
  • Ponder problems  (work, ask about, but do not turn in) (1.1)4, 14; (1.2) 8,16,28; (1.3)10, 14, 38,44; (1.5)6,12,18,24; (1.6)24,28; (1.7) 4,16,24.
  • Consult the main points of the lesson and some review.
  • Play with an app on families of functions
  • Remember to bring your laptop to class.

In class