Half life

**cammywhite** · May 2nd 2009, 05:01 PM

Substance Z has a half-life of 10 years. You currenly have 4 grams of Z.
How much will you have 20 years from now? 25 years from now?

Ok... so after 20 years it will be 1 grams right?

but how come this equation doesn't give me the answer 1 gram?
$Z= (\frac{1}{2})^\frac{t}{10}$

What should be the correct eqution for it?

**TheEmptySet** · May 2nd 2009, 05:05 PM

Originally Posted by cammywhite

Substance Z has a half-life of 10 years. You currenly have 4 grams of Z.
How much will you have 20 years from now? 25 years from now?

Ok... so after 20 years it will be 1 grams right?

but how come this equation doesn't give me the answer 1 gram?
$Z= (\frac{1}{2})^\frac{t}{10}$

What should be the correct eqution for it?

You forgot to multiply by the amount you started with

$y=4\left( \frac{1}{2}\right)^{\frac{t}{10}}$

**skeeter** · May 2nd 2009, 05:06 PM

Originally Posted by cammywhite

Substance Z has a half-life of 10 years. You currenly have 4 grams of Z.
How much will you have 20 years from now? 25 years from now?

Ok... so after 20 years it will be 1 grams right?

but how come this equation doesn't give me the answer 1 gram?
$Z= (\frac{1}{2})^\frac{t}{10}$

What should be the correct eqution for it?

forget the 4?

$Z= 4\left(\frac{1}{2}\right)^\frac{t}{10}$

**cammywhite** · May 2nd 2009, 05:07 PM

Originally Posted by TheEmptySet

You forgot to multiply by the amount you started with

$y=4\left( \frac{1}{2}\right)^{\frac{t}{10}}$

If t = 20 years... then we wiil have 4 grams after 20 years which doesn't make sense cuz it should be depreciating

maybe my calculation is wrong

**TheEmptySet** · May 2nd 2009, 05:09 PM

Originally Posted by cammywhite

If t = 20 years... then we wiil have 4 grams after 20 years which doesn't make sense cuz it should be depreciating

Ummm not quite ...

if $t=20$ we get

$y=4\left( \frac{1}{2}\right)^{\frac{20}{10}}= 4\left( \frac{1}{2}\right)^{2}=4\left( \frac{1}{4}\right)=\frac{4}{4}=1$

**skeeter** · May 2nd 2009, 05:09 PM

Originally Posted by cammywhite

If t = 20 years... then we wiil have 4 grams after 20 years which doesn't make sense cuz it should be depreciating

not so ... remember the order of operations?

**e^(i*pi)** · May 2nd 2009, 05:10 PM

Originally Posted by cammywhite

If t = 20 years... then we wiil have 4 grams after 20 years which doesn't make sense cuz it should be depreciating

$<br /> Z(20) =4\left( \frac{1}{2}\right)^{\frac{20}{10}} = 4 \times \frac{1}{2^2} = 1<br />$

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