First off, I'm assuming the bit after the asterisk in question one was your answer to that question. But that's not quite right. Yes, the halflife of Cesium-137 is ~30 years, but the Cesium was released twice, once in 1986 and again in 2011. By 2041, half of the 2011 Cesium is gone, but some amount still remains from the 1986 disaster.
a) What year will cesium-137 level be half as much as immediately after the 2011 X disaster? *2041
b) In what year will cesium-137 level be a quarter as much as immediately after the 2011 X disaster?
These two questions are basically the exact same question. In 2011, some portion of the 1986 Cesium was still around, plus 4.2 times the amount released in 1986 was released in 2011. You were given the instructions to use A=Pe^(rt). Let's call the amount of Cesium released in 1986
x, then A(2011) = xe^(rt) + 4.2x. Then, given the halflife of cesium, what units make sense to use for
t? And then you can solve for
r based on the fact that after 30 years, exactly half of a given sample will be present. Plug in your values and solve for the Cesium present in 2011, then use that information to find when the amount of Cesium is half (or in part b, a quarter) of that amount.
c) How long after the disaster until cesium-137 levels are the same as immediately after the 1986 Y disaster.
Here, you need to find some year when the amount of Cesium will return to the value in 1986, which we earlier called
x. If we call that unknown year
y, then can you set up an equation to find the amount of Cesium in that year, in terms of the amount in 2011?
