## aküarios 2 years ago how to use "In"?

1. aküarios

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

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

3. satellite73

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

4. satellite73

says QUARTERLY so be careful usually it is monthly

5. aküarios

6. aküarios

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

7. satellite73

divide by 4132.78

8. satellite73

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

9. aküarios

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

10. satellite73

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

11. aküarios

and why is it use in this kind of formulas?

12. satellite73

$1.012^{4t}=1.936$ rounded

13. satellite73

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

14. satellite73

it doesn't matter what log you use

15. aküarios

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

16. satellite73

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

thats the formula right?

18. satellite73

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

19. aküarios

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

20. satellite73

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

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

22. satellite73

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

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

24. aküarios

sorry ... i got 13.8

25. satellite73

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

26. aküarios

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

27. satellite73

what does $$t$$ represent?

28. aküarios

time...

29. aküarios

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

30. satellite73

in what units?

31. aküarios

years&months

32. satellite73

yes t is time in years

33. aküarios

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

Was 13 years and 10 months the correct answer?