My Math Forum Help with exponential functions

 Algebra Pre-Algebra and Basic Algebra Math Forum

 January 31st, 2014, 11:16 PM #1 Newbie   Joined: Dec 2013 From: Seattle, WA Posts: 14 Thanks: 0 Help with exponential functions The problem: "Suppose you deposit $2000 in a savings account that pays interest at an annual rate of 4%. How many years will it take for the account to contain$2500?" So I created the equation, which is y = 2000(1.04)^x My question is, how do I solve this without guessing and checking on my calculator? How do I solve this algebraically? I think I do this: 2500 = 2000(1.04)^x I'm sure I'm incorrect, like always, but what's the next step? PEMDAS?
 February 1st, 2014, 12:33 AM #2 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Help with exponential functions You need to use the natural logarithm: $\ln(2500)= \ln(2000*(1.04)^x)= \ln(2000) + x\ln(1.04)$ $x= \frac{\ln(2500) - \ln(2000)}{\ln(1.04)} = \frac{\ln(1.25)}{\ln(1.04)}$
February 1st, 2014, 12:43 AM   #3
Newbie

Joined: Dec 2013
From: Seattle, WA

Posts: 14
Thanks: 0

Re: Help with exponential functions

Quote:
 Originally Posted by Pero You need to use the natural logarithm:
We never learned how to do that, at least not yet. Looks like a bunch of rubbish mixed with more rubbish. But hey, it's good ol' confusing math. Something that makes me want to scratch my eyes because it makes me feel illiterate.

February 1st, 2014, 03:34 AM   #4
Global Moderator

Joined: Dec 2006

Posts: 21,035
Thanks: 2271

Quote:
 Originally Posted by BlackSnowMarine So I created the equation, which is y = 2000(1.04)^x
Why? There is insufficient information in the wording of the question to justify that equation.

It is possible that the interest is not added to the account, but instead paid to the account holder, in which case the account will never contain $2500. February 1st, 2014, 04:05 AM #5 Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Help with exponential functions Quote:  Originally Posted by BlackSnowMarine The problem: "Suppose you deposit$2000 in a savings account that pays interest at an annual rate of 4%. How many years will it take for the account to contain \$2500?" So I created the equation, which is y = 2000(1.04)^x
This is the equation for interest compounded annually. Are you ever told in the problem that the interest is compounded?
The wording "that pays interest at an annual rate of 4%" makes me think it is simple interest.

Quote:
 My question is, how do I solve this without guessing and checking on my calculator? How do I solve this algebraically? I think I do this: 2500 = 2000(1.04)^x I'm sure I'm incorrect, like always, but what's the next step? PEMDAS?
It would be very strange to work with compound interest and exponentials ($1.04^x$) without learning logarithms. If this were simple interest your equation would be 2500= 2000+ 80x.

 Tags exponential, functions

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post BlackSnowMarine Algebra 3 February 13th, 2014 08:08 PM Logan19 Calculus 5 April 18th, 2012 11:46 PM pomazebog Calculus 2 March 3rd, 2012 08:53 PM bilano99 Calculus 5 December 2nd, 2011 07:01 PM bilano99 Calculus 4 November 29th, 2011 02:30 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top