February 15

objective

• to understand the properties of exponential functions
• how transformations effect the graphs of exponential functions
• how exponential functions are used to explain the models of growth and decay
• to be able to compare the difference in growth of exponentials and polynomials

key ideas and/or vocabulary
laws of exponents, using calculators to study transformations of exponential functions, comparison with other functions, population growth, decay, half-life, e, TANLN (calculator)

solved problems - using key ideas
 

• Sketch family of exponential functions {-2,1,2,3}^x and {1/2,1/3,0.1}^x
• window [-3.15 ,3.15] x [-.5, 5.7]
• Use TANLN to find the slopes of tangent lines at x=0 for 2^x ,3^x ,e^x
•  studying transformations on exponential functions without calculator, #7-14
• transformations on e^x , #15
• What is special about e?  Use of TANLN
• finding exponential equation given the graph, #17
• population growth, #23
• comparison of the difference in growth of exponentials and polynomials,#21
• The half-life of Strontium 90 is 25 years.  If you have 100 mg of Strontium 90, how much will be left after 50 years?

announcements
Homework.  #16,18,20,24
 
 
 

QUESTION OF THE DAY

Use TRACE to find the point at which the graph of the parametric equations intersects itself. x(t) = t2 y(t) = t3 - .5t

SOLUTION

 

SOLUTION.  The graph below is found in a window [-1, 4] x [.125, .875]. The point of intersection is found at (.5,0) and occurs when t ~ .7 and -.7.