SOLUTION: The weight Wt grams, of radioactive substance remaining after t years is given by Wt=1000*2^-0.04t grams. Find the time taken for the weight to:
a. halve
b. reach 1% of its origi
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Question 359107: The weight Wt grams, of radioactive substance remaining after t years is given by Wt=1000*2^-0.04t grams. Find the time taken for the weight to:
a. halve
b. reach 1% of its original value
Thanks :)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Your function:
\ =\ 1000\,\cdot\,2^{-0.04t})
is only valid if you start with a kilogram of a particular substance. The correct general formula for that particular substance is:
\ =\ W_o\,\cdot\,2^{-0.04t})
Where 
is the starting weight of the substance.
If we are interested in the time for the weight to halve, then:
}{W_o}\ =\ \frac{1}{2})
Which is to say:
Take the log of both sides (any base is ok, but you should use either base 10 or base e because those are generally what is supported by your calculator)
\ =\ \ln(0.5))
Use the laws of logarithms
\ =\ \ln(0.5))
Divide by )
}{-0.04\ln\left(2\right)})
The rest is calculator work.
Part b is done the same way, except:
}{W_o}\ =\ 0.01)
John
My calculator said it, I believe it, that settles it
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