(a) The fraction P of strontium remaining as a function of time t can be found using the formula:
P(t) = (100 - 2t) / 100
Here, t represents the number of years elapsed.
(b) To estimate the half-life of strontium, we can set up the equation:
P(t) = 0.5
Substituting the equation from part (a), we get:
(100 - 2t) / 100 = 0.5
Simplifying the equation, we have:
100 - 2t = 50
Solving for t, we find:
2t = 50
t = 25
Therefore, the half-life of strontium is estimated to be 25 years.
(c) To estimate how many grams of strontium will remain after 11 years, we can substitute t = 11 into the equation from part (a):
P(11) = (100 - 2*11) / 100
Simplifying the equation, we have:
P(11) = (100 - 22) / 100
P(11) = 78 / 100
P(11) = 0.78
To find the grams of strontium remaining, we multiply this fraction by the initial amount of strontium, which is given as 5.5 grams:
Grams remaining = P(11) * 5.5
Grams remaining = 0.78 * 5.5
Grams remaining ≈ 4.29 grams
Therefore, after 11 years, approximately 4.29 grams of strontium will remain.