"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?
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: .$\displaystyle P \:=\:P_o(0.965)^t$ . 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: .$\displaystyle \frac{P}{P_o} \;\approx\;80.75\%$