# Math Help - Half-life problem: correct answer?

1. ## Half-life problem: correct answer?

"What is the half-life of a radioactive substance that has a decay rate of 25% per decade?

Hint: Remember that the Rule of 70 does not give a good approximation to half-life when the rate is larger than 15%. We must use the actual formula here."

This what I did.

I used the exact half-life formula:

- log102
_____________________
log10(1+r)

In this case, r= 0.25

After substituting, I get:

0.301030 = -2.4094
________
-01250

Am I right? I'm a bit confused..

Thanks guys.

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2. Originally Posted by c47v3770
"What is the half-life of a radioactive substance that has a decay rate of 25% per decade?

Hint: Remember that the Rule of 70 does not give a good approximation to half-life when the rate is larger than 15%. We must use the actual formula here."

This what I did.

I used the exact half-life formula:

- log102
_____________________
log10(1+r)

In this case, r= 0.25

After substituting, I get:

0.301030 = -2.4094
________
-01250

Am I right? I'm a bit confused..

Thanks guys.

[/size]
Half-life is positive ......

Use the results in post #3 of this thread: http://www.mathhelpforum.com/math-he...ease-help.html

Let initial mass be $N_0$. Substitute $N = \frac{N_0}{4}$ and t = 10 and solve for k. Then substitute $N = \frac{N_0}{2}$ and solve for t (using the value of k you found).

3. Originally Posted by mr fantastic
Half-life is positive ......

Use the results in post #3 of this thread: http://www.mathhelpforum.com/math-he...ease-help.html

Let initial mass be $N_0$. Substitute $N_0 = \frac{N_0}{4}$ and t = 10 and solve for k. Then substitute $N_0 = \frac{N_0}{2}$ and solve for t (using the value of k you found).
"Use the results in post #3 of this thread: Half-life problem. Please help "

I'm not sure of what results to use. Could you please be a bit more specific?

I really appreciate your help.

4. Originally Posted by c47v3770
"Use the results in post #3 of this thread: Half-life problem. Please help "

I'm not sure of what results to use. Could you please be a bit more specific?

I really appreciate your help.
$N=N_0e^{-kt}$.