The algebraic expression: I am not sure how to type this on the computer but in the parenthesis is the square root of t+h - square root of t over h

15.92(square root of t + h - square root of t over h)
models the average rate of change in the percentage of households online from t years after 1997 to t + h years after 1997. Use the expression to solve this problem...

Let t=4 and h=2. Evaluate the expression to find the average rate of change in percentage of households online from 2001-2003 that is, between 4 years and 4 + 2, or 6 years after 1997.

2. Is the expression,
$\displaystyle 15.92\left(\sqrt{t+h} - \sqrt{\frac{t}{h}} \right)$
or
$\displaystyle 15.92\left(\sqrt{t+h} - \frac{\sqrt{t}} {h}\right)$

I wish I could do what you just did with the numbers but it is everything over h. Does that make sense?

4. $\displaystyle \frac{15.92\left(\sqrt{t+h} - \sqrt{t}\right)}{h}$
like this?
Also, do you need this in simplest radical form or decimal

5. Awesome Job

Yes that is how it is written awesome job. Yes to have in simplest form. I have tried several times to get it to work and can't seem to get it yet to work out.

6. Not sure if this helps

I am not sure if this helps at all but my book has a an average rate change of 3.6% but I am not getting it at all? I am lost on this whole radical stuff.

7. $\displaystyle \frac{15.92\left(\sqrt{t+h} - \sqrt{t}\right)}{h}$
$\displaystyle \frac{15.92}{h}\left(\sqrt{t+h} - \sqrt{t}\right)$
$\displaystyle \frac{15.92}{2}\left(\sqrt{4+2} - \sqrt{4}\right)$
$\displaystyle 7.96\left(\sqrt{6} - \sqrt{4}\right)$
$\displaystyle \sqrt{63.3616}\left(\sqrt{6} - \sqrt{4}\right)$
$\displaystyle \sqrt{63.3616}\sqrt{6} - \sqrt{63.3616}\sqrt{4}$
$\displaystyle \sqrt{63.3616\cdot6} - \sqrt{63.3616\cdot4}$
$\displaystyle \sqrt{380.1696} - \sqrt{253.4464}$
$\displaystyle \sqrt{96\cdot3.9601} - \sqrt{64\cdot3.9601}$
$\displaystyle \sqrt{96}\sqrt{3.9601} - \sqrt{64}\sqrt{3.9601}$
$\displaystyle \left(\sqrt{96}-\sqrt{64}\right)\left(\sqrt{3.9601}\right)$
$\displaystyle \left(\sqrt{16\cdot6}-8\right)\left(\sqrt{3.9601}\right)$
$\displaystyle \left(4\sqrt{6}-8\right)\left(\sqrt{3.9601}\right)$

Considering I'm not even in high school, this is as far as I could get without going insane. Maybe Black or Hacker could get you farther.

8. Sorry I messed up

Oh my goodness I am so sorry I meant when I said everything being over h it was supposed to be the parenthesis only and the 15.92 on the side. I am so very sorry. I feel horrible.

9. That's okay, but is this the real expression?
$\displaystyle 15.92\left(\frac{\sqrt{t+h}-\sqrt{t}}{h}\right)$

10. Correct

I can't express how sorry I am. Thank you for helping me.

11. Actually, it doesn't matter, because all three of these are the same thing.
$\displaystyle \frac{15.92}{h}\left(\sqrt{t+h} - \sqrt{t}\right)$

$\displaystyle \frac{15.92\left(\sqrt{t+h} - \sqrt{t}\right)}{h}$

$\displaystyle 15.92\left(\frac{\sqrt{t+h} - \sqrt{t}}{h}\right)}$

So my answers the same, sorry I couldn't finish helping you.

12. Thanks Quick

Thank you for trying. i hope someone else can try to do it too.

13. Originally Posted by Quick
$\displaystyle \frac{15.92\left(\sqrt{t+h} - \sqrt{t}\right)}{h}$
$\displaystyle \frac{15.92}{h}\left(\sqrt{t+h} - \sqrt{t}\right)$
$\displaystyle \frac{15.92}{2}\left(\sqrt{4+2} - \sqrt{4}\right)$
$\displaystyle 7.96\left(\sqrt{6} - \sqrt{4}\right)$
Considering I'm not even in high school, this is as far as I could get without going insane. Maybe Black or Hacker could get you farther.
well done, Quick
just substitute the value of 6^(1/2) and you will get the answer

14. I don't get it??

This is what I have tried to do to come up with 3.6% but am off still??

15.92 (√ t + h -√ t)
h

15.92 (√ 4 + 2 - √ 4)
2
15.92 (√ 6 - √ 4)
2
√ 3.99 √ 6 - √ 3.99 √ 4
√3.99 * 6 - √ 3.99 * 4
√23.94 - √15.96 = √7.98/2 = 3.9

15. Originally Posted by kbryant05
This is what I have tried to do to come up with 3.6% but am off still??

15.92 (√ t + h -√ t)
h

15.92 (√ 4 + 2 - √ 4)
2
15.92 (√ 6 - √ 4)
2
7.96(2.4494 - 2)
= 7.96 * 0.4494
=3.577

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