File under /hs. c= file remove. cmx.html. please refile.
We have been given an equation
. We are asked to solve the equation for t.
First of all, we will divide both sides of equation by a.
![\frac{ae^{ct}}{a}=\frac{d}{a}](https://tex.z-dn.net/?f=%5Cfrac%7Bae%5E%7Bct%7D%7D%7Ba%7D%3D%5Cfrac%7Bd%7D%7Ba%7D)
![e^{ct}=\frac{d}{a}](https://tex.z-dn.net/?f=e%5E%7Bct%7D%3D%5Cfrac%7Bd%7D%7Ba%7D)
Now we will take natural log on both sides.
![\text{ln}(e^{ct})=\text{ln}(\frac{d}{a})](https://tex.z-dn.net/?f=%5Ctext%7Bln%7D%28e%5E%7Bct%7D%29%3D%5Ctext%7Bln%7D%28%5Cfrac%7Bd%7D%7Ba%7D%29)
Using natural log property
, we will get:
![ct\cdot \text{ln}(e)=\text{ln}(\frac{d}{a})](https://tex.z-dn.net/?f=ct%5Ccdot%20%5Ctext%7Bln%7D%28e%29%3D%5Ctext%7Bln%7D%28%5Cfrac%7Bd%7D%7Ba%7D%29)
We know that
, so we will get:
![ct\cdot 1=\text{ln}(\frac{d}{a})](https://tex.z-dn.net/?f=ct%5Ccdot%201%3D%5Ctext%7Bln%7D%28%5Cfrac%7Bd%7D%7Ba%7D%29)
![ct=\text{ln}(\frac{d}{a})](https://tex.z-dn.net/?f=ct%3D%5Ctext%7Bln%7D%28%5Cfrac%7Bd%7D%7Ba%7D%29)
Now we will divide both sides by c as:
![\frac{ct}{c}=\frac{\text{ln}(\frac{d}{a})}{c}](https://tex.z-dn.net/?f=%5Cfrac%7Bct%7D%7Bc%7D%3D%5Cfrac%7B%5Ctext%7Bln%7D%28%5Cfrac%7Bd%7D%7Ba%7D%29%7D%7Bc%7D)
![t=\frac{\text{ln}(\frac{d}{a})}{c}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B%5Ctext%7Bln%7D%28%5Cfrac%7Bd%7D%7Ba%7D%29%7D%7Bc%7D)
Therefore, our solution would be
.
Jacob has 4 balloons, because 4 is half of 8
Hope this helps ya ;)
This is easier to understand with a picture...
We know that a triangle has 3 sides right?
Well, if the perimeter is 39 and there are 3 sides you would divide 39 by the 3 sides
39/3=13
Therefore, one side of the triangle would equal 13