Analysis of a rock sample shows that it contains 6.25% of its original uranium-235. How old is the rock? How do you know?

Explanation:

A radioactive isotope is an isotope that undergoes nuclear decay, breaking apart into a smaller nucleus and emitting radiation during the process.

The half-life of an isotope is the amount of time it takes for a certain quantity of a radioactive isotope to halve.

For a radioactive isotope, the amount of substance left after a certain time t is:

(1)

where

is the mass of the substance at time t = 0

m(t) is the mass of the substance at time t

is the half-life of the isotope

In this problem, the isotope is uranium-235, which has a half-life of

We also know that the amount of uranium left in the rock sample is 6.25% of its original value, this means that

Substituting into (1) and solving for t, we can find how much time has passed:

1. the question asks the most appropriate, which seems to rule out "all of the above." your choice appears to be the correct one.

2. the protocol described is good for identifying correlation, but not cause and effect. for cause/effect, you need to devise a protocol that will assign the treatment (or not) to groups that have essentially the same "demographics" with respect to all the other variables. your choice regarding control group seems appropriate. random assignment of treatment (choice d) may be appropriate also. (i think you can argue that b and d are just different descriptions of the same method.)

3. d will randomize the birds, but may not guarantee there are 10 in each group. e will do both, so seems the better choice.

comment on question 2

based on the problem statement, it seems clear that confident, attentive drivers are more likely to use daytime running lights. so, the protocol might need to be devised in such a way that the lights would be turned on or off without the driver's knowledge. (an attentive driver will figure it out.) assigning a confident, attentive driver to a group required to drive without running lights might mess with his/her confidence and attentiveness. you don't want your experiment to do that. (nor do you want the experiment to subject a driver to greater risk of accident as a consequence of driving without running lights.) experiments involving human safety are always problematic.