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6 – Exponents and Exponential Functions

  • How did that new band become an overnight sensation?
  • Imagine you saw their video and bought their song. Then you told five friends about them. They told five friends, who also told friends and so on.
  • Suddenly the video had millions of views and the band’s debut single had gone platinum.
  • Not exactly a linear graph, is it?
  • But what happened when the news reported the band’s album was delayed?
  • Their popularity faded and sales dropped quickly each week. Again, not a steady linear decline.
  • You need knowledge of exponents and their use in functions to represent nonlinear situations like these.
  • Exponential functions and their graphs allow you to model many types of real-world situations about quantities that increase or decrease proportionally to their value.
  • These models help you make important predictions. For example, how fast will the virus spread?
  • How quickly will my savings grow?
  • What will the population be in ten years?
  • How many teams are left in the tournament after three rounds?
  • How much will the car be worth in seven years?
  • In this unit you’ll learn how a variety of real-world situations like these can be understood using exponential functions.

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