# 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  $f(x) = m x + b: m = (f(x_2)-f(x_1))/(x_2-x_1)$
• 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

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.
• See pages 11-15 on exponential functions.

In class