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## confusedstudent2012 2 years ago 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

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1. satellite73

you want something like $10e^{rt}$ and you are looking for $$r$$ right?

2. confusedstudent2012

yes.

3. satellite73

ah i see the problem you were using the formula for compounding $$n$$ times, but it is continuous compounding

4. confusedstudent2012

so i should be using the A= Pe^rt ?

5. satellite73

so here is what you know when you start you have 10, so you begin with $$10e^{rt}$$

6. satellite73

you also know that when $$t=45$$ you have 30, so replace A by 30 and $$t$$ by 45 and solve for $$r$$

7. satellite73

i.e. solve $30=10e^{45r}$ for $$r$$

8. satellite73

you good from there? divide by 10 get $3=e^{45r}$ then take the log and finally divide by 45

9. satellite73

you could have actually started at that step, reasoning that it triple is 45 minutes

10. confusedstudent2012

so i would have log3= loge^45r ?

11. confusedstudent2012

thank you so much for explaining this to me! :)

12. satellite73

no you would have $\log(3)=45r$

13. confusedstudent2012

i though what you did to once side you did to the other?

14. satellite73

when you take the log of $$e^{45r}$$ you just get $$45r$$

15. confusedstudent2012

oh that's right. there are so many rules

16. satellite73

$e^x=y\iff x=\ln(y)$ they say the same thing

17. satellite73

well i wouldn't call that a "rule" it is equivalent logarithmic form or how one gets a variable out of the exponent

18. satellite73

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

19. confusedstudent2012

to me they all feel like rules and properties right now, probably until get the hang of it more

20. confusedstudent2012

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.

21. satellite73

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

22. satellite73

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 $$t=0$$

23. confusedstudent2012

yes. i do.

24. satellite73

in a line you needed to find $$m$$ in this case you need to find $$r$$

25. confusedstudent2012

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

26. satellite73

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

27. confusedstudent2012

you are so amazing! Thank you for explaining it, makes so much sense!

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