SOLUTION: This is a logarithmic equation not really understanding this. A woman deposits 50,000 in a savings account with 4% continuously compounded interest. How many years must she wait

Click here to see ALL problems on logarithm

Question 236622: This is a logarithmic equation not really understanding this.
A woman deposits 50,000 in a savings account with 4% continuously compounded interest. How many years must she wait until the balance has doubled.
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A woman deposits 50,000 in a savings account with 4% continuously compounded interest. How many years must she wait until the balance has doubled.
-----------------------------------
A(t) = Pe^(rt)
---
Explanation of the variables.
A(t) is the value of the account after t years.
P is the amount initially deposited in the account
e = 2.1718281828... is an irrational number that comes up in
the math modeling of growing or decaying things like money accounts.
r is the yearly interest rate
t is the number of years the account is compounded.
---------------------------------------------------------
100,000 = 50,000*e^(0.04t)
---
e^(0.04t) = 2
Note: The natural log of e^x is x because "ln(e^x)" means
tell me the exponent of e that gives you e^x. The answer is "x".
-----
Take the natural log of both sides to get:
---
ln(e^0.04t) = ln(2)
0.04t = ln2
t = [ln(2)/0.04]
t = 17.33 years
==========================
Cheers,
stan H.

Answer by Edwin McCravy(20064) (Show Source):
You can put this solution on YOUR website!
This is a logarithmic equation not really understanding this.
A woman deposits $50,000 in a savings account with 4% continuously compounded interest. How many years must she wait until the balance has doubled.

Divide both sides by Use the rule: is equivalent to Divide both sides by about 17 years, 4 months. Edwin