Apaleontologist estimates that when a particular rock formed, it contained 12 mg of the radioactive isotope potassium-40. the rock now contains 3 mg of potassium-40. the half-life of patassium-40 is 1.3 billion years. about how old is the rock? a. 0.4 billion yearsb. 0.3 billion yearsc. 1.3 billion yearsd. 2.6 billion yearse. 5.2 billion years

d. 2.6 billion years.

Explanation:

The half-life of a radioactive element it's the time that its mass decreases by half, or, by 0.50. So, if there is 10 mg of A when the mass became 5 mg, it will have past one half-life. The next half-life will decrease by half the actual mass, so it will give 2.5 mg, which is 0.5x0.5 of the initial mass.

So, the number of half-life (n) can be calculated for:

Where M is the residual mass and Mo the inital mass, so:

n = 2

So, it has passed 2 half-lives. If one half-life is 1.3 billion years, two must be 2.6 billion years, which is the age of the rock.

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.

i would say b

explanation:

but i think i would need more information than that