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Do Homework - Sadia Mahama-Google Chrome Secure I https://www.m c open helcem Student player Homework aspx?homeworkla-43 17269 74 &questionid;=9&Rushed;=fal b ddn45 tant acort ran -yes MAT 128 3071 Homework: Section 4.4 Homework #18 Score: 0 of 1 pt 4.4.76 lf 60% of a radioactive element remains radioactive after 300 milion years then what percent ema s adosete a er t What percent remains radioactive after 700 milion years? Do not round until the inal answer Then round to the nearest integer as neoded ) bsPlus" Courses se Home se Outline e Lecture Notes element? work s & Tests Pian 90110 (B complete) Hw Score: 80%, 8 of 10 pts Question Help 11 nysas, what she hari est it ook r Contents Success r SuccesS dia Library

Explanation / Answer

applying exponential formula

A = P e^rt

0.6 = e^(3*10^8) r

taking natural log on both sides

ln 0.6 = 3*10^8r ln e

r = -1.7027 * 10^-9

percent remaining after 700 million years

A = Pe^rt

let x percept remains

xP = P e^(-1.7027 * 10^-9 * 7*10^8 )

x = e^-1.1919

x = 0.3036

that rounds to 30%

percent remaining after 700 million years is 30%

half life is

1/2 = e^(-1.7027 * 10^-9 t )

ln 1/2 = -1.7027 * 10^-9 t

so half life is

t = 407087085.546 years

which is around 407 million years

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