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# Exponential Function

### Module 23: Exponential Functions

Explaination | Example |
---|---|

Basic x^n= x*x*x*x..........x (multiple x with itself n number of times) | x^4=x*x*x*x |

Negative Exponents x^-n=x*x*x*x..........x (first take the reciprocal, then multiple x with itself n number of times) | x^-4=1/x*x*x*x |

Multiplying with Exponents x^n x^m=x^n+m (when multiplying numbers with exponents add the exponents) | x^4*x^7=x^4+7=x^11 |

Dividing with Exponents x^n/ x^m=x^n-m (when dividing numbers with exponents subtract the exponents) | x^7/x^4=x^7-4=x^3 |

Powering with Exponents (x^n)^m=x^n*m ( when powering numbers with exponents multiply the exponents) | (x^2)^3=x^2*3=x^6 |

Exponents as a Fraction x^1/n (when fractions are exponents take the n root of the number) | x^1/2= square root of x |

Exponential Growth y=A(1+r)^t A=Amount r=Rate t=Time | A=500, r=.25, t=3 y=500(1+ .25)^3=976.5625 |

Exponential Decay y=A(1-r)^t A=Amount r=Rate t=Time | A=400, r=.50, t=4 y=400(1- .50)^4=25 |

Exponents to the Power of Zero x^0=1 ( anything to the power of zero will always be 1) | 4586^0=1 |

Fraction with Exponents (x/y)^n=(x^n)/(y^n) (take the numerator to the power of n and the denominator to the power of n) | (x/y)^5=(x^5)/y^5 |

Solve (a^4)(b^6)(c^11)*(a^8)(b^10)(c^16) | a^4 +8=a^12 b^6+10=b^16 c^11+16=c^27 (a^12)(b^16)(c^27) |

Solve (x^10)^8 | x^10*8=x^80 |

Solve 27^1/3=x | 27^1/3 3*3*3=27 x=3 |

Created by:
DHollis