Question

how to use "In"?

Answer 1

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?

Answer 2

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

Answer 3

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

Answer 4

says QUARTERLY so be careful
usually it is monthly

Answer 5

yah u right... misread

Answer 6

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

Answer 7

divide by 4132.78

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

and why is it use in this kind of formulas?

Answer 12

\[1.012^{4t}=1.936\] rounded

Answer 13

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

Answer 14

it doesn't matter what log you use

Answer 15

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

Answer 16

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

Answer 17

thats the formula right?

Answer 18

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

Answer 19

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

Answer 20

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
\[b^x=A\iff x=\frac{\ln(A)}{\ln(b)}\]

Answer 21

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

Answer 22

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

Answer 23

haha got it...

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

Answer 24

sorry ... i got 13.8

Answer 25

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

Answer 26

got it...

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

Answer 27

what does \(t\) represent?

Answer 28

time...

Answer 29

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

Answer 30

in what units?

Answer 31

years&months

Answer 32

yes t is time in years

Answer 33

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...

Answer 34

Was 13 years and 10 months the correct answer?