Sure, I'd be happy to help with parts (b) and (c)!
(b) To estimate the half-life of strontium, we need to find the time it takes for half of the substance to decay. In this case, we know that the decay rate is 2 percent per year. So let's set up an equation to find the half-life:
(0.98)^t = 0.5
To solve for t, we can take the logarithm of both sides of the equation:
t * log(0.98) = log(0.5)
Now, we can solve for t:
t = log(0.5) / log(0.98)
Using a calculator, we find that t ≈ 35.16 years. So, the estimated half-life of strontium is approximately 35.16 years.
(c) To estimate how many grams of strontium will remain after 38 years, we can use the fraction P(t) = (.98)^t that we derived in part (a). We know that initially there were 6 grams of strontium, so we can plug in t = 38 into the equation to find the remaining amount:
P(38) = (.98)^38
Using a calculator, we find that P(38) ≈ 3.1115 grams. Therefore, it is estimated that approximately 3.1115 grams of strontium will remain after 38 years.
Remember, these estimates assume the decay rate remains constant at 2 percent per year.