Math 115  Lab   M. Flashman Monday Sept. 30, 2002 12:00-12:50

---

• Exponentials
• Discuss how each constant b, k, A, and C effects the graph.[>1, >0, <0.]
• f(x)= b^x Use b animator; family
• b^(kx)
• b^(x-s)
• Ab^(kx)
• Ab^(kx) + C
• f(x) = exp(x): estimate e by finding b that matches this graph.
  
  
• Logs
• f(x)  = log(x)
• f(x) = ln(x)
• logb(x) = ln(x)/ln(b) [user-defined functions]
• y =1 where does logb(x) crosses y= 1. Use this to estimate e.
  
  
• Graphing compositions
• Ax+C into and out of exp and ln.
• Exp(-x^2)
• ln(exp(x))
• exp(ln(x))
  
  
• Solving equations
• Find A and k if y=Ae^(kx) with y(1)=20, y(2)= 50.
• Find x if ln(x) +ln(x+1) = 5 ; slider, table, solver
  
  
• Logarithmic scales
• Y= log(a), X= log(a)  family a = 1 to 100  11 steps
• Y= log(Ab^x) = xlog(b)+ log(A)  : log- linear scales
• Y = log(Ax^p) = plog(x)+log(A) : log log scales

(log(t), log(a*t^b))