Functions - Exponential Functions

- Exponential FunctionsObjective: Solve Exponential equations by finding a common our study of algebra gets more advanced we begin to study more involvedfunctions. One pair of inverse Functions we will look at are Exponential functionsand logarithmic Functions . Here we will look at exponentialfunctions and then wewill consider logarithmic Functions in another lesson. Exponential Functions arefunctions where the variable is in the exponent such asf(x) =ax. (It is importantnot to confuse Exponential Functions with polynomial Functions where the variableis in the base such asf(x) =x2).World View NoteOne common application of Exponential Functions is popula-tion growth. According to the 2009 CIA World Factbook, the country with thehighest population growth rate is a tie between the United Arab Emirates (northof Saudi Arabia) and Burundi (central Africa) at There are 32 countrieswith negative growth rates, the lowest being the Northern Mariana Islands (northof Australia) at exponetial equations cannot be done using the skillset we have seen inthe past.

9 9 Dividebothsidesby9 x = 5 9 OurSolution As we multiply exponents we may need to distribute if there are several terms involved. Example 3. 273x+5 = 814x+1 Rewrite27as33 and81as34 (92 wouldnotbesamebase) (33)3x+5 =(34)4x+1 Multiplyexponents3(3x +5) and4(4x +1) 39x+15 =316x+4 Samebase, setexponentsequal 9x + 15 = 16x +4 Movevariablestooneside

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  Functions, Exponential, Exponent, Functions exponential functions

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