"Suppose a radioactive substance decays at a rate of 3.5% per hour. What percent of the substnce is left after 6 hours?"

Can you please list what I would have to do to solve this problem?

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- Jan 6th 2013, 09:14 PMEJdive43Can someone help me with this expoential decay problem?
"Suppose a radioactive substance decays at a rate of 3.5% per hour. What percent of the substnce is left after 6 hours?"

Can you please list what I would have to do to solve this problem? - Jan 6th 2013, 11:49 PMchiroRe: Can someone help me with this expoential decay problem?
Hey EJdive43.

Does it decay continuously or only in hourly intervals? - Jan 7th 2013, 07:30 AMSorobanRe: Can someone help me with this expoential decay problem?
Hello, EJdive43!

Quote:

A radioactive substance decays at a rate of 3.5% per hour.

What percent of the substance is left after 6 hours?

First, set up the function.

The substance loses 3.5% every hour.

That is, 96.5% of the substance remains.

We have: .$\displaystyle P \:=\:P_o(0.965)^t$ . where $\displaystyle \begin{Bmatrix} P_o &=& \text{original amount} \\ t &=& \text{time (in hours)} \end{Bmatrix}$

When $\displaystyle t = 6$, we have: .$\displaystyle P \:=\:P_o(0.965^6) $

. . . . . . . . . . . . . . . . .$\displaystyle P \:=\:P_o(0.807539696)$

. . . . . . . . . . . . . . . .$\displaystyle \frac{P}{P_o} \:=\:0.807539696$

Therefore: .$\displaystyle \frac{P}{P_o} \;\approx\;80.75\%$