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# Module 23

### Exponential Functions

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

Solve for X 4^X=1024 | X=5 |

Solve for X 5^X=625 | X=4 |

Solve for X 4^X=32 | X=5/2 |

Solve for X 16^X=32 | X=32 |

Solve for X 10000^X=100000 | X=10 |

Solve for X 64^5X=16^X+3 | X=6/13 |

An item weighs 4040 lbs and has a decay rate of 1.41.4% per day. How much will still remain after 5050 days? Use: Y=40(0.986)^X let x be 5050. | 19.77 lbs would remain |

The equation y=118.74118.74(1.129)^ X gives the number of cell phone users (in millions) in 1 country for the years of 2002-2009. X=0 corresponds to 2002, x=1 corresponds to 2003, and so on. Predict the number of cell phone users in 2011 | 353.9 million cell phone users in 2011 |

If b>0 and b doesn't equal 1 than B^X=B^Y is equivalent to | X=Y |

Exponential Function is | A function of the form f(x)=b^X if b>0 if b is not 1 and X is a real number |

Why don't we want the base b to be 1? | It would be a constant function. Any number times 1 will equal 1 |

Why don't we want the base b to be a negative number? | We want real numbers, not complex numbers, |

27^x+1=9 | x= -1/3 |

Exponential Function Graph | f(x)=b^x, b>0, b doesn't equal 1 -one to one function -y intercept (0,1) -no x intercept |

Exponential Function domain is | (- infinity, infinity) |

Exponential Function range is | (0, infinity) |

The graph is a decreasing graph if | b is between 0 and 1 |

The graph is an increasing graph if | b>1 |

Steps to solve 16^x=8 | Make bases the same (2^4)^x=2^3 Simplify 2^4x=2^3 Set exponents equal 4x/4=3/4 x=3/4 |

A quantity that grows or decays by the same percent at regular time intervals is said to | Grow exponentially or decay exponentially |

Exponential Decay formula | Y=C(1-r)^x C=original amount R=growth rate (often a percent, turn into a decimal before adding into equation) X=number of time intervals (1-r)= growth factor |

Exponential Growth formula | Y=C(1+r)^x C=original amount R=growth rate ( often a percent, turn into decimal before adding into equation) X= number of time intervals (1+r)= growth factor |

Half life is | the amount of time it takes for half of something to decay or disappear |

How to find X for half life in equation y=C(1-r)^X? | number of years/half life= X |

In the formula for half life y=C(1-r)^X what is r? | r is the growth rate, in the formula for half life r is 50% which is written into decimal form 0.50 |

Original amount=305, Growth rate=5%, # of years=8 What is the amount in 8 years? (round to the nearest whole #) | y=305(1+0.05)^8 The amount in 8 years is around 451 |

Current employees= 640, percent decreasing per year=5%, How many employees will there be in 10 years? (round to the nearest whole 3) | y=640(1-0.05)^10 There will be around 383 employees left in 10 years |

Original amount=21 grams, half life=152, #of years=500, What is x? How many grams will there be left (round to nearest whole number? | 500 (years) /152 (half life)=3.3 (time interval) x=3.3 Y=21(1-0.50)^3.3= around 2.1 grams will be left |

The equation y=109.54(1.107)^x gives the number of cellular phone users y (in millions) in a country for the years 2002 through 2009. If x=0 corresponds to 2002, x=1 corresponds to 2003, What is the number of cell phone users in the year 2014 | In the year 2014 the number of cell phone users in the country will be about 371 million |

Find the amount Sam owes at the end of 6 years if $5600 is loaned to her at a rate of 7 % compounded monthly. Use A=P(1+r/n)^nt | The amount owed is 8512.59 |

Created by:
SamLarzelere