# Thread: Can someone help me with this expoential decay problem?

1. ## Can 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?

2. ## Re: Can someone help me with this expoential decay problem?

Hey EJdive43.

Does it decay continuously or only in hourly intervals?

3. ## Re: Can someone help me with this expoential decay problem?

Hello, EJdive43!

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

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

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

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

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