Question

Modeling Exponential Growth and Decay Madeleine Younes A wooden artifact from an archaeological dig contains 76 percent of the carbon-14 that is present in living trees. To the nearest year, about how many years old is the artifact? (HINT: The half-life of carbon-14 is 5730 years.) The artifact is approximately years old. For additional help with this problem type, access the following resources: • TEXT Read Modeling Exponential Growth and Decay • VIDEO Watch this video on modeling exponential growth and decay. · LAB Ask one of our Peer Learning Assistants for help. (Do this last!)

Answer 1

Sale Given data- Archaeological dig contains 76% of the caption Half lite of capbon –14 : 5730 yrs * General Exponential decay function is given as M = Mocetto where M = 10% t= 5730 yrs & Substitute these two values o in egun his = M. e(5730) : . -^[57307 - multiplying "en" on both sides In( 32)In.e-[54307 5 en (12) = - 5730. lnce) RE InCY2) = -4.573001 lnile): 1 x = ln (2) - 5730 0.000121)

Then in -0.000121.6 412 4() → when dia contains 46% of cagbon ::1:76. Mo re: 0.76 oto ] equation ☺ >> Substitute il value in 0.00012707 0.76. Mo - Mile) 0.0001211 ) 0176 = sidų; then In on both => - multiplying Melltiplying * In (0.76) : Inie 0.000121 () Inle) in 10.76): ~ 0.00012117) en.(0.76) = -0.000127.17), . ln(0.76) -0.000121 10.2:1443684570176 0.00012) The certifact is approlimt E 2268.07