Question

I'm posting this question for @redheadangel. -Will medal for answer-

Answer 1

Thank You!

Answer 2

np :)

Answer 3

@quickstudent and @ltrout can you help them?

Answer 4

do you know the formula for "continuous compounding" ?

Answer 5

Yes: A=Pe^n

Answer 6

you mean
\[ A = P e^{r t}\]
if we put in numbers
r= 0.045
\[ 14000= 12500 e^{0.045t}\]

Answer 7

oh yeah, that's right. But where do i go from there? What variable am i trying to find?

Answer 8

they want you to "solve for t"
the first step is divide both sides by 12500

Answer 9

ohh okay, so you are left with: .112=e^.045t

Answer 10

and then what

Answer 11

that seems wrong 14000 is bigger than 12,500 so you should get a number bigger than 1

Answer 12

oh whoops! I meant: 1.12

Answer 13

next you use the idea
\[ \ln(e^x) = x\]
so "take the natural log" of both sides

Answer 14

hmm.. i dont think i know how to take the natural log

Answer 15

1.12=e^.045t

like this:
ln(1.12) = ln( e^(0.045t) )

on the right side (of the =) use the "rule" ln(e^x) = x to simplify it

Answer 16

so, wouldnt it just be 0,045 if it equals x? (im sorry if im being slow)

Answer 17

on the right side, you "bring down" the exponent which is 0.045t (note the "t" is also part of the exponent)

Answer 18

okay what after it is brought down , it is multiplied to the e?

Answer 19

no.
by definition ln(e^x) = x ln(e)
and ln(e) = 1 (so we usually just write the "rule" as ln(e^x) = x

Answer 20

ohh okay, then i think the answer would be around: 2.5 hours?

Answer 21

ln(1.12) = ln( e^(0.045t) )
ln(1.12) = 0.045 t
now divide both sides by 0.045
ln(1.12)/0.045 = t

we need a calculator
or type into google
ln(1.12)/0.045=

Answer 22

yes thats what i did and got 2.5 app.

Answer 23

would you help me with one more? last one I promise, I cant seem to get it right

Answer 24

Thanks phi :)

Answer 25

Oh yeah and thank you again @Cas_fangirl_14

Answer 26

as a check we can do
12500*e^(0.045*2.5)=

that gives
13988.40 which is close to 14000
so we need to be more accurate to get 14000
the actual answer depends how accurately they want it.

Answer 27

I think approxamently, so we should be goood