A radioactive substance decays exponentially at a rate of 7% per hour. How long do you have to wait until the substance has decayed to 1/4 of its original size

Question

I would like to know how to solve this 

Answer 1

Hi Alexa;

 

If it decays at 7% per hour, then each hour the total is 93% of the previous total

1/4 = 0.25

 

0.25s = s(0.93)^h

where s represents beginning substance amount, h = hours elapsed

 

0.25 = 0.93^h

log 0.25 = log 0.93^h

log 0.25 = h[log 0.93]

 

h = [log 0.25/log 0.93]

 

h = 19.1 hours