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The dollar value of two investments after t years is given by:

  • $f(t)=1800\cdot1.055^t$
  • $g(t)=9500\cdot1.041^t$

Solve the equation $f(t) = g(t)$.

What does your solution tell you about the investments?

This is what I have so far:

$1800\cdot1.055^t=9500\cdot1.041^t\implies$

$1800/9500=1.055/1.041$

Am I setting this up correctly so far?

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    No, you are not. – 2017-01-17
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    @Arthur: I edited the entire post. Don't you consider that helpful? – 2017-01-17
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    @barakmanos Oh, right. I missed that. I apologize. – 2017-01-17
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    I really have no idea how to edit my posts to the like of above. I am brand new to this website but if I knew how to HTML wise I would have. – 2017-01-17
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    @Alex You can click the "edit" button on the bottom left of your post and see what your post looks like right now (then click "cancel" if you're afraid to change anything, or improve something if you feel it needs to). For more information on how we write mathematics on this site (we don't use HTML), you could, for instance, see [this guide](http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference). – 2017-01-17
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    I looked at the edit history. barakmanos, you made it look much better which is helpful. Still, the OPs question and his initial steps were there even before the edit. And I think he deserves better than telling him "No, you are not". We are all here to learn, on whatever level. – 2017-01-17
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    Thank you so much Arthur, I will check that guide out! I had no idea. Sorry for any confusion. Now I see the setup properly. – 2017-01-17

2 Answers 2

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Hint:

$$1800\cdot1.055^t=9500\cdot1.041^t$$

$$\left(\frac{1.055}{1.041}\right)^t=\frac{9500}{1800}$$

Take logarithm and solve for $t$.

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    I see the setup more clearly now. Thank you for the help! – 2017-01-17
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You have $1800(1.055)^t=9500(1.041)^t$

Dividing both sides by $1800$ and $1.041^t$

$\frac{1.055^t}{1.041^t}=\frac{9500}{1800}$

Here you have mixed something up.

$\left( \frac{1.055}{1.041}\right)^t=\frac{9500}{1800}$

Taking logs

$\log \left[ \left( \frac{1.055}{1.041}\right)^t\right]=\log\left( \frac{9500}{1800}\right)$

$t\cdot \log \left[ \frac{1.055}{1.041}\right]=\log\left( \frac{9500}{1800}\right)$

Thus $$t=\frac{\log\left( \frac{9500}{1800}\right)}{\log \left[ \frac{1.055}{1.041}\right]}=124.523\approx 125$$