It's crazy that we are already at the end of Chapter 6 and will be reviewing and taking the test next week because it feels like we just started this new chapter. This week, we focused on using separation of variables to find the function of a given derivative that passes through a specific point. Separation of variables is helpful when anti-differentiating with both x and y variables. This section has required me to look back and remember basic algebra skills that I may not have used in a while, which may have been the part that caused me to get stuck on some problems. The rules about natural logarithms were the ones that I found most important in remembering. It was nice to get a little reminder and refresh my memory on these skills, and I think I have these types of problems down pretty well now. Separation of variables seems to me a lot like implicit differentiation, only backwards, and thinking about it in this way helps me to take the right steps in solving these kinds of problems.
The second part of section 6.4 that we worked on this week looked at exponential growth and radioactive decay. It's funny because this is a lot like what we are learning in AP Chem right now! The equation that we solved for to use for finding half life is actually the same equation that is in our notes in AP Chem. In Calc, we used the idea that 1/2 y(the initial amount of radioactive nuclei) = y * e^-kt to find that t = ln 2/k, and in Chem, we were given the equation: t(half-life) = 0.693/k. I think it's cool that what we are learning in each class happened to overlap at the same time, and learning how and why the half-life equation is what it is is helpful for both classes. When working on the chem homework, I was actually able to use ideas and equations that I used on the Calc assignment, and I was really excited because I actually understood one part of the chem assignments that are always so ridiculous and impossible.
Overall, I feel pretty good about Chapter 6 and think I am ready for the test. I am glad that we have a day to review on Monday to make sure I have everything down!
The second part of section 6.4 that we worked on this week looked at exponential growth and radioactive decay. It's funny because this is a lot like what we are learning in AP Chem right now! The equation that we solved for to use for finding half life is actually the same equation that is in our notes in AP Chem. In Calc, we used the idea that 1/2 y(the initial amount of radioactive nuclei) = y * e^-kt to find that t = ln 2/k, and in Chem, we were given the equation: t(half-life) = 0.693/k. I think it's cool that what we are learning in each class happened to overlap at the same time, and learning how and why the half-life equation is what it is is helpful for both classes. When working on the chem homework, I was actually able to use ideas and equations that I used on the Calc assignment, and I was really excited because I actually understood one part of the chem assignments that are always so ridiculous and impossible.
Overall, I feel pretty good about Chapter 6 and think I am ready for the test. I am glad that we have a day to review on Monday to make sure I have everything down!