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## aküarios Group Title how to use "In"? one year ago one year ago

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1. aküarios Group Title

I have this question.. and I know i Have to use In... but dont know how Brooklyn has a goal to save $8,000 to buy a new entertainment system. In order to meet that goal, she deposited$4,132.79 into a savings account. If the account has an interest rate of 4.8% compounded quarterly, approximately when will Brooklyn be able to make the purchase?

2. aküarios Group Title

8000 = 4132.79(1+.048/12)^12*t 8000 = 4132.79(1.004)^12t (now I get stuck here..

3. satellite73 Group Title

$4132.79\times (1+\frac{.048}{4})^{4t}=8,000$

4. satellite73 Group Title

says QUARTERLY so be careful usually it is monthly

5. aküarios Group Title

yah u right... misread

6. aküarios Group Title

but then how do you continue... because that's when I get lost :/

7. satellite73 Group Title

divide by 4132.78

8. satellite73 Group Title

then use the change of base formula $b^x=A\iff x=\frac{\ln(A)}{\ln(b)}$

9. aküarios Group Title

what actually In use for... like, I understand nothing at all about In... (In=log right) ?

10. satellite73 Group Title

$4132.79\times (1+\frac{.048}{4})^{4t}=8,000$ $4132.79\times (1.012)^{4t}=8,000$ $1.012^{4t}=8,000\div 4132.79$

11. aküarios Group Title

and why is it use in this kind of formulas?

12. satellite73 Group Title

$1.012^{4t}=1.936$ rounded

13. satellite73 Group Title

the to solve for $$4t$$ use $4t=\frac{\log(1.936)}{\log(1.012)}$

14. satellite73 Group Title

it doesn't matter what log you use

15. aküarios Group Title

mmm... but why log? like.. what is its function? I never understood when the teacher explained it...

16. satellite73 Group Title

then i am sure i cannot explain it in a chat box here but basically $b^x=y\iff \log_b(y)=x$

17. aküarios Group Title

thats the formula right?

18. satellite73 Group Title

it is a way to solve for a variable that is in the exponent

19. aküarios Group Title

mmmm.. got it.. the answer I got for the formula is t= 10.8 (then years and 8 month?)

20. satellite73 Group Title

but you only have two logs on your calculator, $$\log_{10}(x)$$ log base ten and $\ln(x)=\log_e(x)$ which is log base e so if you want an actual decimal for an answer, you have to use $b^x=A\iff x=\frac{\ln(A)}{\ln(b)}$

21. aküarios Group Title

in my calculator i have log2, log10, and In... can use any true? (I used In)

22. satellite73 Group Title

in other words, to solve for the variable in the exponent, it is the log of the total divided by the log of the base that is how to solve for a variable that is in the sky

23. aküarios Group Title

haha got it... so my answer is 10.8... how do i convert that into years and months?

24. aküarios Group Title

sorry ... i got 13.8

25. satellite73 Group Title

makes no difference, all logs are the same $\log_b(x)=\frac{\log_a(x)}{\log_a(b)}$

26. aküarios Group Title

got it... but how do you convert t = 13.85 into years and months?

27. satellite73 Group Title

what does $$t$$ represent?

28. aküarios Group Title

time...

29. aküarios Group Title

so im guessing it would be 13 years and 8 months right?

30. satellite73 Group Title

in what units?

31. aküarios Group Title

years&months

32. satellite73 Group Title

yes t is time in years

33. aküarios Group Title

but in the choices I've got there is no 13 years and 8 month... (they have 13 years and 10 months) so I'm guessing is that one.. but they also have 13 years and 5 months... so like, i want to know how to solve it correctly...

34. murrcat Group Title

Was 13 years and 10 months the correct answer?