SOLUTION: I don't know how to solve this word problem: The half life of carbon-14 is 5715 years. Prehistoric cave paintings were discovered in a cave in France. The paint contained 15% if t

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I don't know how to solve this word problem: The half life of carbon-14 is 5715 years. Prehistoric cave paintings were discovered in a cave in France. The paint contained 15% if t      Log On


   

Question 1140288: I don't know how to solve this word problem:
The half life of carbon-14 is 5715 years. Prehistoric cave paintings were discovered in a cave in France. The paint contained 15% if the original carbon-14. Estimate the age of paintings.
I'm supposed to be using one of these formulas:
y=k(a)^x
At=Ao(1+r)^t
At=Ao(e)^rt
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You can select the form of the model that you want.

Halflife given as 5715 years
A=A%5Bo%5De%5E%28-kt%29
1%2F2=1%2Ae%5E%28-kt%29
ln%281%2F2%29=-kt
ln%282%29=kt
k=ln%282%29%2Ft
k=ln%282%29%2F5715------------k=0.0001213

model can then be highlight_green%28A=A%5Bo%5De%5E%28-0.0001213t%29%29.


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The paint contained 15% if the original carbon-14. Estimate the age of paintings.
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This means 0.15=1%2Ae%5E%28-0.0001213t%29, and similar to some of the steps shown above, you can solve for t.

Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.

Read the lesson
    - Using logarithms to solve real world problems
in this site, Problem on Carbon dating.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Logarithms".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.