anonymous
  • anonymous
how to use "In"?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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?
anonymous
  • anonymous
8000 = 4132.79(1+.048/12)^12*t 8000 = 4132.79(1.004)^12t (now I get stuck here..
anonymous
  • anonymous
\[4132.79\times (1+\frac{.048}{4})^{4t}=8,000\]

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anonymous
  • anonymous
says QUARTERLY so be careful usually it is monthly
anonymous
  • anonymous
yah u right... misread
anonymous
  • anonymous
but then how do you continue... because that's when I get lost :/
anonymous
  • anonymous
divide by 4132.78
anonymous
  • anonymous
then use the change of base formula \[b^x=A\iff x=\frac{\ln(A)}{\ln(b)}\]
anonymous
  • anonymous
what actually In use for... like, I understand nothing at all about In... (In=log right) ?
anonymous
  • anonymous
\[4132.79\times (1+\frac{.048}{4})^{4t}=8,000\] \[4132.79\times (1.012)^{4t}=8,000\] \[1.012^{4t}=8,000\div 4132.79\]
anonymous
  • anonymous
and why is it use in this kind of formulas?
anonymous
  • anonymous
\[1.012^{4t}=1.936\] rounded
anonymous
  • anonymous
the to solve for \(4t\) use \[4t=\frac{\log(1.936)}{\log(1.012)}\]
anonymous
  • anonymous
it doesn't matter what log you use
anonymous
  • anonymous
mmm... but why log? like.. what is its function? I never understood when the teacher explained it...
anonymous
  • anonymous
then i am sure i cannot explain it in a chat box here but basically \[b^x=y\iff \log_b(y)=x\]
anonymous
  • anonymous
thats the formula right?
anonymous
  • anonymous
it is a way to solve for a variable that is in the exponent
anonymous
  • anonymous
mmmm.. got it.. the answer I got for the formula is t= 10.8 (then years and 8 month?)
anonymous
  • anonymous
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 \[b^x=A\iff x=\frac{\ln(A)}{\ln(b)}\]
anonymous
  • anonymous
in my calculator i have log2, log10, and In... can use any true? (I used In)
anonymous
  • anonymous
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
anonymous
  • anonymous
haha got it... so my answer is 10.8... how do i convert that into years and months?
anonymous
  • anonymous
sorry ... i got 13.8
anonymous
  • anonymous
makes no difference, all logs are the same \[\log_b(x)=\frac{\log_a(x)}{\log_a(b)}\]
anonymous
  • anonymous
got it... but how do you convert t = 13.85 into years and months?
anonymous
  • anonymous
what does \(t\) represent?
anonymous
  • anonymous
time...
anonymous
  • anonymous
so im guessing it would be 13 years and 8 months right?
anonymous
  • anonymous
in what units?
anonymous
  • anonymous
years&months
anonymous
  • anonymous
yes t is time in years
anonymous
  • anonymous
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...
anonymous
  • anonymous
Was 13 years and 10 months the correct answer?

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