Exponential Growth

Transcript

Exponential GrowthWe saw how folding paper multiple times can reach us to the moon. Since thickness doubles after every fold After 2 folds, New thickness = 4 × Old thickness = 2 × 2 × Old thickness After 3 folds, New thickness = 8 × Old thickness = 2 × 2 × 2 × Old thickness We see that 2 is being multipled every time FOLD THICKNESS 0 0.001 cm 1 0.002 cm 2 0.004 cm 3 0.008 cm 4 0.016 cm 5 0.032 cm 6 0.064 cm 7 0.128 cm 8 0.256 cm 9 0.512 cm 10 1.0 cm 11 2.0 cm 12 4.1 cmWe can also write After 2 folds, New thickness = 22 × Old thickness After 3 folds, New thickness = 22 × Old thickness After 10 folds, New thickness = 210 × Old thickness After n folds, New thickness = 2n × Old thickness FOLD THICKNESS 0 0.001 cm 1 0.002 cm 2 0.004 cm 3 0.008 cm 4 0.016 cm 5 0.032 cm 6 0.064 cm 7 0.128 cm 8 0.256 cm 9 0.512 cm 10 1.0 cm 11 2.0 cm 12 4.1 cmThus, we can say that thickness of the paper is growing exponentially. We use the same concept in Investments, and in Compounding In this chapter, we study Exponents, and everything related to that. But first, let’s listen to the Chessboard story