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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 446 (page 1066)

The half-life of radioactive iodine is 60 days. How much of a 50 mg sample will be left in 40 days?

Short Answer

Expert verified

The amount left in 40 days will be $79.37 m g .$

Step by step solution

01

Step 1. Given information

Half-life of iodine $= 60 d a y s$

Initial sample $= 50 m g$

Time for decay $= 40 d a y s$

02

Step 2. Writing the concept.

An amount $A_{0}$ that grows or decays at rate k for certain time t, will be given by:

03

Step 3. Calculation

Put the values of respective variables in the given formula:

$A = 2 A_{0} t = 60 2 A_{0} = A_{0} e^{60 k} e^{60 k} = \frac{2 A_{0}}{A_{0}} e^{60 k} = 2 T a k i n g \log a r i t h m b o t h s i d e s . \ln e^{60 k} = \ln 2 60 k . \ln e = \ln 2 k = \frac{\ln 2}{60} N o w s u b s t i t u t e A_{0} = 50, t = 40 A = 50 e^{40 . \frac{1}{60} \ln 2} = 50 e^{\frac{2}{3} \ln 2} = 79.37 m g$

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