SOLUTION: A storage tank contains niobium-97m, a radioactive element.the percentage of the element that remains is halved each hour. let p=f(t) be the percentage of niobium-97m that remains

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: A storage tank contains niobium-97m, a radioactive element.the percentage of the element that remains is halved each hour. let p=f(t) be the percentage of niobium-97m that remains       Log On


   

Question 1149888: A storage tank contains niobium-97m, a radioactive element.the percentage of the element that remains is halved each hour. let p=f(t) be the percentage of niobium-97m that remains at t hours since the element was placed in the tank.
A) find an equation of f
B)what is the p-intercept of the model? what does it mean in this situation?
C) find f(9). what does it mean in this situation?
D) what is the half-life of niobium-97m?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A) Since p = f(t) is the percentage that remains after t hours, the initial value is 100. Then that percentage is multiplied by 1/2 each hour. So

ANSWER: f%28t%29+=+100%2A%28.5%29%5Et

B) The p-intercept is f(0) = 100. It states the obvious fact that in the beginning 100% of the element remains.

C) f%289%29+=+100%2A%28.5%29%5E9+=+100%2F2%5E9+=+100%2F512 which is approximately 1/5 or 0.2. It means after 9 hours only about 0.2% of the element remains.

D) From the statement of the problem, the half-life is 1 hour.