Homework Help: Algebra word problem

Posted by Soph. on Thursday, October 25, 2007 at 10:06pm.

please help me with the following:

The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model a=3000e^0.053t When will the account be worth $5097?

Algebra word problem - drwls, Thursday, October 25, 2007 at 10:26pm
Set 3000e^0.053t = $5097
e^0.053t = 5097/3000 = 1.699
Take the natural log of both sides
.053 t = 0.53
t = _?_ years
Algebra word problem - Soph., Thursday, October 25, 2007 at 11:12pm
I got 10 years, but my answer choices are: a. 2010, b.2011, c.2009, d. 2012.
And I dont understand how you took the natural log of both sides?
Algebra word problem - drwls, Thursday, October 25, 2007 at 11:25pm
You add t to the year 2000 in this case, so the answer is a.
Taking the natural log (to base e) was in my case done with a hand calculator. The natural log of e^x is x.

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