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Algebra and trigonometry
   ALGEBRA & TRIGONOMETRY  To use logarithms to solve application problems involvingexponentialgrowthanddecay.A colony of humans settles on a previously uninhabited planet. After  t   years, theirpopulation,P,is givenbyequationP=100 e 0.05t  . PROBLEM ST TEMENTOBJECTIVE .b) Whatisthepopulationafter25 years?c) Howlongdoesittakethepopulationto reach2 million?Given P=100 e 0.05t  , METHODOLOGY     When t  =0, P=100 e 0.05(0) =100Therefore, y-intercept is 100.  P a) SOLUTIONS 100 t So, it takes approximately 198 years toreach2 millionpopulation.a) A natural logarithmic function is a logarithmic function with base  e , log e  x   = ln  x  ,where  x   >0.b) We can apply exponential and logarithm functions in our daily life which theyare very useful for example in this case, we are able to find the population of humansinaperiod.Mathematics is the language with which God wrote the universe. —Galileo CONCLUSION
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