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log question - HSN forum

# log question

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### #1jambo david

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Posted 25 April 2006 - 07:56 PM

In a radioactive substance, the mass m grams and time t years is given by m=m0e^(-0.03t), where m0 is the original mass

a)If the original mass is 400 grams, what is the mass after 5 years?
b)How long does it take for the substance to decay to half its original mass?

### #2Dave

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Posted 25 April 2006 - 08:03 PM

a) work out t=1,2,3,4,5
b) 200 = 400 e^(-0.03t)

1/2 = e^(-0.03t)

taking logs of boths side will cancel out the e part leaving you to solve for t

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### #3Steve

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Posted 25 April 2006 - 08:17 PM

For part (a), all you have to do is find m when t = 5. This is because the formula tells you the mass after t years. Also is the original mass, so .
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### #4jambo david

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Posted 25 April 2006 - 08:56 PM

QUOTE(Steve @ Apr 25 2006, 09:17 PM)

For part (a), all you have to do is find m when t = 5. This is because the formula tells you the mass after t years. Also is the original mass, so .

i get that it goes to 400e^-0.15 but i don't understand what to do after that

### #5Dave

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Posted 25 April 2006 - 09:00 PM

that is the value for the new m. For a decimal answer you would use a calculator

cant believe i didnt say what steve said. I just not thinking these days anyhooo

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