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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!

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 $\displaystyle t$?

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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 :/

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.

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Re: Equation problem (high school level math)

Hey mate!

Thanks so much for your help!! I think I got it:

Attachment 25643

Right? :P

Re: Equation problem (high school level math)

I would finish it as:

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

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

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

$\displaystyle t=\frac{2000\ln\left(\frac{3}{2} \right)}{21}\approx38.6157245817$

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!