exponentials

• inverse functions:

  1. rewrite f(x) as y
  2. swap every x with a y and every y with an x
  3. solve for y
  4. write y as f^-1(x)

  methods to solve:

  • ordered pairs- interchange (x,y) coordinates
  • graph- reflect the graph over y=x
  • equation- interchange y and x, solve for y
• exponential models are used to describe the growth of populations, and the rate of change in population size
• how to translate an exponential model:

  1. find the initial value of the population
  2. find the initial value of the rate of change of the population
• $y=$$a(b)^x$exponential function
• rate % model:$y=$$a(1+-r)^x$