# Equation problem (high school level math)

• Nov 10th 2012, 10:50 PM
HenryMerrild
Equation problem (high school level math)
Hey guys :) Math newbie here.

I've been given an assignment, where I am to solve the equation, eg find t:

Attachment 25635

I've divided by 2,70 on both sides, but after that I'm completely lost. If someone could post a step-by-step solution, I'd be very happy!
Thank you all

/Cheers!
• Nov 10th 2012, 10:58 PM
MarkFL
Re: Equation problem (high school level math)
We don't normally post solutions, but will help you to get the solution. You have divided through by 2,70, and so you have:

$\displaystyle \frac{1,5}{2,70}=1-e^{-0,021t}$

I would simplify the left by observing:

$\displaystyle \frac{1,5}{2,70}=\frac{15}{27}=\frac{5}{9}$ and so we have:

$\displaystyle \frac{5}{9}=1-e^{-0,021t}$

What do you think is a good next step towards isolating the variable $\displaystyle t$?
• Nov 10th 2012, 11:18 PM
HenryMerrild
Re: Equation problem (high school level math)
Hey mate,
Thank you for your respons. I've tried a bit, but I'm still completely lost. I'm sure I'm doing something wrong.
I would use the rule:

Attachment 25636

To get:

Attachment 25637
And then use log to find t, but I know that's wrong :/
• Nov 10th 2012, 11:25 PM
MarkFL
Re: Equation problem (high school level math)
The next thing you want to do is isolate the exponential term on one side, and everything else on the other.

Try adding $\displaystyle e^{-0,021}-\frac{5}{9}$ to both sides.
• Nov 11th 2012, 04:57 AM
HenryMerrild
Re: Equation problem (high school level math)
Hey mate!
Thanks so much for your help!! I think I got it:

Attachment 25643

Right? :P
• Nov 11th 2012, 07:24 AM
MarkFL
Re: Equation problem (high school level math)
I would finish it as:

$\displaystyle e^{-0,021t}=\frac{4}{9}$

$\displaystyle e^{0,021t}=\frac{9}{4}$

$\displaystyle 0,021t=\ln\left(\frac{9}{4} \right)=2\ln\left(\frac{3}{2} \right)$

$\displaystyle t=\frac{2000\ln\left(\frac{3}{2} \right)}{21}\approx38.6157245817$
• Nov 11th 2012, 08:03 AM
HenryMerrild
Re: Equation problem (high school level math)
Ah, thank you:) Yours is closer to the answer giving in my book (actually, the same), so I'll use that from now on!
Thank you for helping!