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confusedstudent2012 Group Title

You are growing yeast for a science experiment. You start with 10 ml. You set the experiment up, go away and return 45 minutes later. When you come back, your have 30 ml. Find the rate at which it is growing. The EXACT answer (no calculator necessary) can be given in the form a ln(b). So I do know the answer to this, I got it wrong on the test i took last week, but I am hoping someone can explain to me the process of how to get the answer. I had used to A=(1+r/n)^(nt) but i ended up getting so lost in the problem that I left it blank

  • one year ago
  • one year ago

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  1. satellite73 Group Title
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    you want something like \[10e^{rt}\] and you are looking for \(r\) right?

    • one year ago
  2. confusedstudent2012 Group Title
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    yes.

    • one year ago
  3. satellite73 Group Title
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    ah i see the problem you were using the formula for compounding \(n\) times, but it is continuous compounding

    • one year ago
  4. confusedstudent2012 Group Title
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    so i should be using the A= Pe^rt ?

    • one year ago
  5. satellite73 Group Title
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    so here is what you know when you start you have 10, so you begin with \(10e^{rt}\)

    • one year ago
  6. satellite73 Group Title
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    you also know that when \(t=45\) you have 30, so replace A by 30 and \(t\) by 45 and solve for \(r\)

    • one year ago
  7. satellite73 Group Title
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    i.e. solve \[30=10e^{45r}\] for \(r\)

    • one year ago
  8. satellite73 Group Title
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    you good from there? divide by 10 get \[3=e^{45r}\] then take the log and finally divide by 45

    • one year ago
  9. satellite73 Group Title
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    you could have actually started at that step, reasoning that it triple is 45 minutes

    • one year ago
  10. confusedstudent2012 Group Title
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    so i would have log3= loge^45r ?

    • one year ago
  11. confusedstudent2012 Group Title
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    thank you so much for explaining this to me! :)

    • one year ago
  12. satellite73 Group Title
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    no you would have \[\log(3)=45r\]

    • one year ago
  13. confusedstudent2012 Group Title
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    i though what you did to once side you did to the other?

    • one year ago
  14. satellite73 Group Title
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    when you take the log of \(e^{45r}\) you just get \(45r\)

    • one year ago
  15. confusedstudent2012 Group Title
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    oh that's right. there are so many rules

    • one year ago
  16. satellite73 Group Title
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    \[e^x=y\iff x=\ln(y)\] they say the same thing

    • one year ago
  17. satellite73 Group Title
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    well i wouldn't call that a "rule" it is equivalent logarithmic form or how one gets a variable out of the exponent

    • one year ago
  18. satellite73 Group Title
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    don't forget you are trying to solve for a variable that is in the sky (exponent) algebra will not do that for you you need logs for that

    • one year ago
  19. confusedstudent2012 Group Title
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    to me they all feel like rules and properties right now, probably until get the hang of it more

    • one year ago
  20. confusedstudent2012 Group Title
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    that makes sense. thank you so much! i hate when i get a problem wrong on a test and i can't figure out where i went wrong.

    • one year ago
  21. satellite73 Group Title
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    hope it is clear though. you are looking for \(r\) and it is an exponent that is why this is different from algebra. you need to take the log to get it

    • one year ago
  22. satellite73 Group Title
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    you remember finding the equation of a line given two points? this is analogous to that \(b\) is the \(y\) intercept, what you get when \(x=0\) in this case \(P\) is the \(y\) intercept, what you get when \(t=0\)

    • one year ago
  23. confusedstudent2012 Group Title
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    yes. i do.

    • one year ago
  24. satellite73 Group Title
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    in a line you needed to find \(m\) in this case you need to find \(r\)

    • one year ago
  25. confusedstudent2012 Group Title
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    that actaully makes so much sense to me. i am always trying to bring the r and t down like numerical exponents and solving them algebraically. .. which is usually wrong

    • one year ago
  26. satellite73 Group Title
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    and you do it almost like you do with a line if you have \(y=4x+b\) and you did not know \(b\) you could find it if say \((3,5)\) is on the graph by saying \[5=4\times 3+b\] and solving for \(b\) this is almost the same we know \((45,30)\) is on the graph so you can solve \[30=10e^{45r}\] for \(r\) using the log

    • one year ago
  27. confusedstudent2012 Group Title
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    you are so amazing! Thank you for explaining it, makes so much sense!

    • one year ago
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