Calculating Half Life and such. Please help.

[Ninimoony]

Our env professor gave us homework on calculating half life but gave us literally no lessons on how to do it whatsoever so his very words were "find out how to do it yourself" and "do whatever you can to find out these answers AND show work". So since I Googled it and there are multiple different ways to do it that confuse me, can someone please help me answer these questions with work or link me to somewhere I can post to get help? Thank you.

Questions:
1. A human piece of pottery is dated at 42250 years old by using carbon-14. How many half lives have passed since the pottery was made?

2. What would the percentage of potassium-40 (parent compound) be in a rock that was dated at 250 million years?

3. The concentration of the radioactive isotope in a rock sample is found to me 6.25%. What is the age of the rock?

4. A rock is found to contain 2.2 grams of uranium-235, a radioactive isotope. If the rock has undergone 2.75 half lives, what was the original amount of plutonium-244 in the rock and how old is the rock?

5. An igneous rock originally has 4 grams of uranium-238 in it. When dates the rock only contains 2.4 grams. What are the parent and daughter concentrations (in percentage) and what is its age?

Ive cried, pulled at my own hair, and it sounds ridiculous but math has definitely emotionally scarred me my whole life because its always made me feel like I am stupid/dull/not good enough. So this is an absolute nightmare for me and please just someone help me out.

 

[stapel]

Our env professor gave us homework on calculating half life but gave us literally no lessons on how to do it whatsoever so his very words were "find out how to do it yourself" and "do whatever you can to find out these answers AND show work". So since I Googled it and there are multiple different ways to do it that confuse me, can someone please help me answer these questions with work or link me to somewhere I can post to get help? Thank you.

Questions:
1. A human piece of pottery is dated at 42250 years old by using carbon-14. How many half lives have passed since the pottery was made?

2. What would the percentage of potassium-40 (parent compound) be in a rock that was dated at 250 million years?

3. The concentration of the radioactive isotope in a rock sample is found to me 6.25%. What is the age of the rock?

4. A rock is found to contain 2.2 grams of uranium-235, a radioactive isotope. If the rock has undergone 2.75 half lives, what was the original amount of plutonium-244 in the rock and how old is the rock?

5. An igneous rock originally has 4 grams of uranium-238 in it. When dates the rock only contains 2.4 grams. What are the parent and daughter concentrations (in percentage) and what is its age?

A good place to start might be with lessons covering the topic of "half-life" word problems. Unfortunately, it is not reasonably feasible to attempt here to provide the missing hours of classroom instructions. Fortunately, on the other hand, there are loads of great resources available online through "search engines" (sites with scripts, or "engines", which "search" the Internet for topical material), such as the lessons which are listed here:

. . . . .Google results for "half-life word problems"

For instance, the first lesson in the list gives the following equation for all exponential-growth and -decay exercises:

. . . . .\(\displaystyle A\, =\, Pe^{rt}\)

...where "P" is the starting amount, "r" is the growth or decay rate, "t" is the amount of time, and "A" is the ending amount. The lesson provides many worked-out exercises, complete with detailed explanations.

Once you have studied at least two lessons from the listing, please attempt the exercises. If you get stuck, you can then reply with a clear listing of your efforts so far, at which point we can begin to work with you.

Thank you!