SOLUTION: The half-time of Silicon-10 is 710 years. Right now there is 40g. How much it would be after 700 years?

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Question 687656: The half-time of Silicon-10 is 710 years. Right now there is 40g. How much it would be after 700 years?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the half-life formula is:

0.5+=+e%5E%28tk%29

t+=+half-life_+time

k+=+decay+constant

Use what is given to find the decay+constant.

Given:

half-life of silicon-32 is 710+years

it means: +t+=+710

Plug this into the equation.

0.5+=+e%5E%28tk%29

0.5+=+e%5E%28710k%29

Take the natural logs of both sides.

ln%280.5%29+=+ln+e%5E710k

ln%280.5%29+=+710k

k+=+ln%280.5%29+%2F+710

k+=+-0.693147181+%2F+710

k+=+-0.000976263635


A+=+Pe%5E%28kt%29

A+=+ending_+amount where

P+=+starting_+amount

t+=+half-life+_time

k+=+decay_+constant


Plug in your known values.



A+=+40+%2A+0.5049052230

A+=+20.19620892


Rounded to three decimal places:

A ≈ +20.196g

ANSWER: +20.196g