In my solution paper, the professor simplified the top equation to the bottom equation. Can someone please explain how he was able to do that? View attachment 34203
I presume this is what you got AFTER 'exponentiating'.
[imath]\frac{N}{100- N}= e^{t+100c}[/imath] .......................................incorrect equation
Multiply both sides by 100- N
[imath]N= (100- N)e^{t+ 100c}[/imath]
Distribute on the right.
[imath]N= 100e^{t+ 100c}- Ne^{t+ 100c}[/imath]
Add [imath]Ne^{t+ 100c}[/imath] to both sides
[imath]N+ Ne^{t+ 100c}= 100e^{t+ 100c}[/imath]
Factor out N on the left
[imath]N(1+ e^{t+100c})= 100e^{t+ 100c}[/imath]
Finally, divide both sides by [imath]1+ e^{t+ 100c}[/imath]
[imath]N= \frac{100e^{t+ 100c}}{1+ e^{t+ 100c}}[/imath]
I see that the moderator has marked the first equation as "incorrect equation". I presume that is because I lost the "2". It should be
[math]\frac{N}{100- N}= e^{2t+ 100c}[/math].
To fix that, add a "2" to "t" throughout so that the final result is [math]N= \frac{100e^{2t+ 100c}}{1+ e^{2t+ 100c}}[/math]
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