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Find the exact value of the logarithmic expression. log36 C. 36 D. 12 26

Find the exact value of the logarithmic expression. log36 C. 36 D. 12 26

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A fossilized leaf contains 28% of its normal amount of carbon 14. How old is the fossil to the nearest year? Use 5600 years as the half-life of carbon 14. A. 34,552 B. 10,284 O C. 26,921 OD. 2,654
Transcribed Image Text:A fossilized leaf contains 28% of its normal amount of carbon 14. How old is the fossil to the nearest year? Use 5600 years as the half-life of carbon 14. A. 34,552 B. 10,284 O C. 26,921 OD. 2,654
Find the exact value of the logarithmic expression. log 6 36 A. 2 O B. 6 O C. 36 O D. 12
Transcribed Image Text:Find the exact value of the logarithmic expression. log 6 36 A. 2 O B. 6 O C. 36 O D. 12
Expert Solution
Step 1

Given,

Fossilized leaf contain 28% of its normal amount of carbon -14 

Half life of carbon -14 = 5600 years

We have to find the how old the fossil is .

 

 

Step 2

Let's assume

The normal amount of  carbon -14  =  N

Decay constant = k 

Half life of  carbon -14  =  0.693k = 5600 

So,

k= 0.6935600

Leaf contain the amount of carbon - 14 = n =  N×28100 = 0.28N 

We have the decay equation ; n =Ne-kt 

Where t is the time in years

Substituting the values in the above equation

0.28N = Ne-0.693t5600

0.28 = e-0.693t5600 

Taking logarithm both sides

ln(0.28) = lne-0.6935600t   

-1.273 = -0.6935600t                         because lnab = blna

t = 5600×1.2730.693

t = 10284

So,

The correct option is B                                             Answer

 

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