数学人教A版（2019）必修第一册4.4.1对数函数的概念

对数函数的概念衰减率问题1个单位的C-13按固定年衰减率0.2衰减1年后，衰减了多少？

保留了多少？2年后，衰减了多少？

保留了多少？3年后，衰减了多少？

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数据验证1.上述死亡年数和碳14含量的对应关系只针对部分数据成立吗？2.若设生物死亡年数为n，死亡生物体内碳14含量为t，对于[0,+∞)内所有的n值和相应的t值都满足这个关系吗？3.你能否通过计算[0,+∞)上所有的n对应的t值来验证？

年数C14含量年数C14含量年数C14含量年数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......图象操作验证-函数操作验证1.剥离实际问题对集合A2的限制，从数学中使代数式有意义角度分析，如果将底数⭐换成其他不等于1的正数，集合A2和集合B2有什么变化？2.t还是n的函数吗?操作验证指数对数在at=b(a>0且a≠1)中已知底数a和指数t求幂指数幂运算at已知指数t和幂b求底数开方运算已知底数a和幂b求指数对数运算logab数据验证1.上述碳14含量和死亡年数的对应关系只针对部分数据成立吗？2.若设死亡生物体内碳14含量为t，生物死亡年数为n，对于(0,1]内所有的t值和相应的n值都满足这个关系吗？3.你能否通过计算(0,1]上所有的t对应的n值来验证？

C14含量年数C14含量年数C14含量年数C14含量年数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操作验证操作验