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aküarios Group TitleBest ResponseYou've already chosen the best response.0
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?
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
8000 = 4132.79(1+.048/12)^12*t 8000 = 4132.79(1.004)^12t (now I get stuck here..
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\[4132.79\times (1+\frac{.048}{4})^{4t}=8,000\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
says QUARTERLY so be careful usually it is monthly
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
yah u right... misread
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
but then how do you continue... because that's when I get lost :/
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
divide by 4132.78
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
then use the change of base formula \[b^x=A\iff x=\frac{\ln(A)}{\ln(b)}\]
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
what actually In use for... like, I understand nothing at all about In... (In=log right) ?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\[4132.79\times (1+\frac{.048}{4})^{4t}=8,000\] \[4132.79\times (1.012)^{4t}=8,000\] \[1.012^{4t}=8,000\div 4132.79\]
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
and why is it use in this kind of formulas?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\[1.012^{4t}=1.936\] rounded
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the to solve for \(4t\) use \[4t=\frac{\log(1.936)}{\log(1.012)}\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
it doesn't matter what log you use
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
mmm... but why log? like.. what is its function? I never understood when the teacher explained it...
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
then i am sure i cannot explain it in a chat box here but basically \[b^x=y\iff \log_b(y)=x\]
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
thats the formula right?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
it is a way to solve for a variable that is in the exponent
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
mmmm.. got it.. the answer I got for the formula is t= 10.8 (then years and 8 month?)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
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 \[b^x=A\iff x=\frac{\ln(A)}{\ln(b)}\]
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
in my calculator i have log2, log10, and In... can use any true? (I used In)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
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
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
haha got it... so my answer is 10.8... how do i convert that into years and months?
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
sorry ... i got 13.8
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
makes no difference, all logs are the same \[\log_b(x)=\frac{\log_a(x)}{\log_a(b)}\]
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
got it... but how do you convert t = 13.85 into years and months?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
what does \(t\) represent?
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
so im guessing it would be 13 years and 8 months right?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
in what units?
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
years&months
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
yes t is time in years
 one year ago

aküarios Group TitleBest ResponseYou've already chosen the best response.0
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...
 one year ago

murrcat Group TitleBest ResponseYou've already chosen the best response.0
Was 13 years and 10 months the correct answer?
 one year ago
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