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# Exponent Function

### exponential functions

Question | Answer |
---|---|

f(x)=b^x | exponential function such that b>0, b is not 1,and x is a real number.base constant. |

review of exponents:x^-n=1/x^n (if x not 0),x^1/n= the nth root of x. | for more exponent rules see p337-339 book or www.mathsisfun.com/algebra/exponent-laws.html |

graph by coming up with ordered pair solutions and plot. hint see back | pick at least 4 points & not all of them close to 0 to get proper curvature of graph. |

properties of f(x)=b^x b>0, b not 1:one-to- one function, y-intercept (0,1), cont'd | no x intercept,domain: (-infinity,infinity),range (0,infinity) |

graphs showing increase and decrease see page 724 course book. cont'd | other graph examples see,www.purplemath.com/modules/graphexp3.htm |

A=P(1+r/n)^nt Compound Interest Formula | P-amt loan,r-rate interest,n-# of times interst compounded ea yr,t-duration of loan |

radioactive decay (in chapter 12 formula is provided) ex. y=30(27)^-0.004t | 30 is amt in pounds & t-time,duration,y-how much in pounds will remain after t days.pg.726 |

uniqueness of b^x | let b>0 & b not 1.Then b^x=b^y is equivalent to x=y |

Created by:
walkerd