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aküarios
 one year ago
Best ResponseYou've already chosen the best response.0I 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?

aküarios
 one year ago
Best ResponseYou've already chosen the best response.08000 = 4132.79(1+.048/12)^12*t 8000 = 4132.79(1.004)^12t (now I get stuck here..

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1in 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

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

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

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

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

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

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

aküarios
 one year ago
Best ResponseYou've already chosen the best response.0but 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...

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