數(shù)學(xué)人教A版（2019）必修第一冊(cè)4.4.1對(duì)數(shù)函數(shù)的概念

對(duì)數(shù)函數(shù)的概念衰減率問題1個(gè)單位的C-13按固定年衰減率0.2衰減1年后，衰減了多少？

保留了多少？2年后，衰減了多少？

保留了多少？3年后，衰減了多少？

保留了多少？......6.8年后，保留了多少？

0.20.86.80.830.8×0.20.82×0.20.820.8數(shù)據(jù)驗(yàn)證1.上述死亡年數(shù)和碳14含量的對(duì)應(yīng)關(guān)系只針對(duì)部分?jǐn)?shù)據(jù)成立嗎？2.若設(shè)生物死亡年數(shù)為n，死亡生物體內(nèi)碳14含量為t，對(duì)于[0,+∞)內(nèi)所有的n值和相應(yīng)的t值都滿足這個(gè)關(guān)系嗎？3.你能否通過計(jì)算[0,+∞)上所有的n對(duì)應(yīng)的t值來驗(yàn)證？

年數(shù)C14含量年數(shù)C14含量年數(shù)C14含量年數(shù)C14含量01......2000.30.78508......57300.50000......100000.29829......10.99988......2001.40.78497......57310.49994......100010.29826......20.99976......2002.50.78487......57320.49988......100020.29822......30.99964......2003.60.78476......57330.49982......100030.29818......40.99952......2004.70.78466......57340.49976......100040.29815......50.99940......2005.80.78456......57350.49970......100050.29811......60.99927......2006.90.78445......57360.49964......100060.29808......70.99915......20080.78435......57370.49958......100070.29804......80.99903......2009.10.78424......57380.49952......100080.29800......90.99891......2010.20.78414......57390.49946......100090.29797......100.99879......2011.30.78403......57400.49940......100100.29793......110.99867......2012.40.78393......57410.49934......100110.29790......120.99855......2013.50.78383......57420.49927......100120.29786......130.99843......2014.60.78372......57430.49921......100130.29782......140.99831......2015.70.78362......57440.49915......100140.29779......150.99819......2016.80.78351......57450.49909......100150.29775......160.99807......2017.90.78341......57460.49903......100160.29772......170.99795......20190.78330......57470.49897......100170.29768......180.99782......2020.10.78320......57480.49891......100180.29764......190.99770......2021.20.78310......57490.49885......100190.29761......圖象操作驗(yàn)證-函數(shù)操作驗(yàn)證1.剝離實(shí)際問題對(duì)集合A2的限制，從數(shù)學(xué)中使代數(shù)式有意義角度分析，如果將底數(shù)?換成其他不等于1的正數(shù)，集合A2和集合B2有什么變化？2.t還是n的函數(shù)嗎?操作驗(yàn)證指數(shù)對(duì)數(shù)在at=b(a>0且a≠1)中已知底數(shù)a和指數(shù)t求冪指數(shù)冪運(yùn)算at已知指數(shù)t和冪b求底數(shù)開方運(yùn)算已知底數(shù)a和冪b求指數(shù)對(duì)數(shù)運(yùn)算logab數(shù)據(jù)驗(yàn)證1.上述碳14含量和死亡年數(shù)的對(duì)應(yīng)關(guān)系只針對(duì)部分?jǐn)?shù)據(jù)成立嗎？2.若設(shè)死亡生物體內(nèi)碳14含量為t，生物死亡年數(shù)為n，對(duì)于(0,1]內(nèi)所有的t值和相應(yīng)的n值都滿足這個(gè)關(guān)系嗎？3.你能否通過計(jì)算(0,1]上所有的t對(duì)應(yīng)的n值來驗(yàn)證？

C14含量年數(shù)C14含量年數(shù)C14含量年數(shù)C14含量年數(shù)10......0.5554867.293......0.3558561.245......0.1316865.7760.9870.978......0.5445032.782......0.3448821.447......0.12916929.6120.89963.343......0.5335201.651......0.3339090.106......0.12816993.9440.881056.753......0.5225374.043......0.3229367.790......0.12717058.7810.871151.230......0.5115550.106......0.3119655.127......0.12617124.1300.861246.799......0.55730......0.39952.813......0.125171900.851343.486......0.4895913.896......0.28910261.620......0.12417256.3990.841441.317......0.4786101.977......0.27810582.412......0.12317323.3360.831540.320......0.4676294.437......0.26710916.156......0.12217390.8190.821640.523......0.4566491.484......0.25611263.944......0.12117458.8580.811741.955......0.4456693.343......0.24511627.009......0.1217527.4610.81844.648......0.4346900.255......0.23412006.754......0.11917596.6380.791948.632......0.4237112.480......0.22312404.788......0.11817666.3990.782053.941......0.4127330.296......0.21212822.960......0.11717736.7540.772160.609......0.4017554.007......0.20113263.418......0.11617807.7130.762268.671......0.397783.941......0.1913728.671......0.11517879.2860.752378.165......0.3798020.454......0.17914221.680......0.11417951.4840.742489.128......0.3688263.934......0.16814745.965......0.11318024.3180.732601.601......0.3578514.803......0.15715305.767......0.11218097.8000.722715.626......0.3468773.524......0.14615906.249......0.11118171.941操作驗(yàn)證操作驗(yàn)