Really need help on a math problem! (Logarithm & Exponential Functions) :D
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Really need help on a math problem! (Logarithm & Exponential Functions) :D

[From: ] [author: ] [Date: 12-01-13] [Hit: ]
log[base 1.log2/log1.n=8.I figured if it was compounded weekly,0.16 years.......
1. If you invested money into an account that pays 9% compounded weekly, how many years would it take for your deposit to double?

We're in the unit "Exponential and Logarithmic Functions"

I would really appreciate it if you could help me! :D

This is what I did:

y=a(1+b)^n

where b is percentage, n is variable for time, a is initial value and y is final value.

I decided to plug in values to see what the numbers would become.

200=100(1+0.09)^n

2=(1.09)^n

then from exponential to logarithm converted to

log[base 1.09] (2)=n

then

log2/log1.09=n

n=8.04

I figured if it was compounded weekly, it would be 8 weeks = 2 months

Then 2 months/12 months per year

0.16 years.

I might have done something wrong, Thanks!

-
amount = principal(1 + 0.09/52)^52t . . . let the principal = 1
2 = (1 + 0.09/52)^52t
2 = (1.00173)^52t
In2 = 52t*In(1.00173) . . . taking natural log of both sides and using properties of logarithms
In2/In(1.00173) = 52t
401.00958 = 52t
t = 7.71 years

The quick method for continuous compounding is In2/rate = 7.7 years
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