Math help please!!!!!?

Question

1.Maya has deposited $600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double?

2. write the logarithmic equation in exponential form. For example, the exponential form of "log5 25 = 2" is "52 = 25".

log 3 27 = 3

log 125 25 = 2/3

Answer 1

Hi,

1.Maya has deposited $600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double?

A = Pe^(rt)

1200 = 600e^(.0564t)

2 = e^(.0564t)

ln 2 = ln e^(.0564t)

ln 2 = .0564t

ln (2)/.0564 = t

t = 12.29

It will take 12.29 years for her money to double. <==ANSWER

2. write the logarithmic equation in exponential form. For example, the exponential form of "log5 25 = 2" is "52 = 25".

log 3 27 = 3

3³ = 27 <==ANSWER

log 125 25 = 2/3

125^(⅔) = 25 <==ANSWER

I hope that helps!! :-)

Answer 2

The formula for continuous compounding is:

FV = P*e^(i*t)

FV = future value

P = initial payment

i = continuous interest rate

t = number of years

1200 = 600e^(5.64%*t)

2 = e^(5.64%*t)

ln 2 = 5.64%*t

t = (1/5.64%)*ln 2

t = 12.28984363 years

Answer 3

well the formula for compound interest i believe is

principal*e^(rate*time) = future value so your principal is 600 your interest is 5.64% and you want to double your money so your future value is 1200 so your formula would look like this:

600*e^(.0564*t) = 1200

and now solve for "t" we start by dividing the whole thing by 600 so we end up with:

e^(.0564*t)=2 now take the natural logarithm of both sides which would be LN so you can get rid of that "e" so you get

Ln(e)^(.0564*t) = Ln(2)  and Ln(e) cancells so you get

.0564=Ln(2)/.0564 just plug that into your calculator and you should get your "t" or how long it would take which i think would be:

12.29 years

now log 3 27 = 3 is just written as 3^3=27 the base is the first number the "3" thats the number you start off with the middle number the "27" will be the number you set the equation to and the last number of the problem will be the exponent of the first number which happens to be a 3 as well so the second problem

log 125 25 = 2/3 first number is 125 so thats our base (our first number on our answer) second number is 25 thats what our answer will be set equal too so we have 125 = 25 so far and the last number on the problem is 2/3 so that will be the exponent of our base (our first number of our answer) so our answer is

125^(2/3)=25

hope this helps good luck

Answer 4

(1+5.64/100)^n=2,then nLog (1.0564)=Log 2,n=Log2 / Log1.0564=

0=Log2/Log1.0564=12.63 years.

O.K.