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Phy 231
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
q006 b3 and b4 how to build fx
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From B3. Precalculus
Question: `q006. If the population of the frogs in your frog pond increased by 10% each month, starting with an initial population of 20 frogs, then how many frogs would you have at the end of each of the first three months (you can count fractional frogs, even if it doesn't appear to you to make sense)? Can you think of a strategy that would allow you to calculate the number of frogs after 300 months (according to this model, which probably wouldn't be valid for that long) without having to do at least 300 calculations?
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####My question is how do I come up with a function that can be used to calculate the number of frogs after x amount of months. I can see that the amount of frogs increase 10% from the month before, and can calculate that for the first few months linearly, but cant figure it out for say 20 months without doing 20 calculations first.
####Just a description of how the mechanics work would suffice. I want to do this first, frogs = 20 + 1.10*(number of months), but that only works if i do the previous calculations and change my initial value of 20.
I know it is frogs = 20*1.10^t, what is confusing is the 1.10^t. ####I ran into the same problem with the decreasing gold rate problem in B5 q006.
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Every month you multiply the number of frogs by 1.10, as I believe you understand.
If you multiply the number of frogs by 1.10, then multiply that result by 1.10, you have multplied twice by 1.10, so you have multiplied by 1.10^2.
If you multiply by 1.10 again, you will have multiplied by 1.10 ^3.
It is clear how this extends. If you multiply by 1.10 a total of t times, you will have multiplied by 1.10^t.
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B3. Precalculus.q006 Can you think of a strategy that would allow you to calculate the number of frogs after 300 months.
B4. Calculus q.006 Question: `q006. Suppose that every week you go to the jeweler and obtain a certain number of grams of pure gold, which you then place in an old sock and bury in your backyard. Assume that buried gold lasts a long, long time, that the the gold remains undisturbed, and that no other source adds gold to your backyard.
####3. Answer the same question assuming that every week you bury half the amount you did the previous week.
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This depends on your understanding of geometric sequences, which is a typical precalculus topic.
I gave someone an extended note on the gold question. If that was you, please resubmit the question along with my note, so I don't repeat everything a second time.
If it wasn't you, resubmit that question anyway, plus any insights you get from my answer to the frog question, and let me know that you didn't get that note. I can send you a copy of the note along with additional commentary.
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