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January 31st, 2014, 11:16 PM   #1
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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?
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February 1st, 2014, 12:33 AM   #2
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Re: Help with exponential functions

You need to use the natural logarithm:



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February 1st, 2014, 12:43 AM   #3
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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.
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February 1st, 2014, 03:34 AM   #4
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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.
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February 1st, 2014, 04:05 AM   #5
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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 () without learning logarithms. If this were simple interest your equation would be 2500= 2000+ 80x.
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