<h2>4. Create a table, write an equation, AND show all your work.</h2>
Currently the stock is $62 and has been decreasing 3% each month. So, if we call
the first month then:

So the Table is:
![\left[\begin{array}{cc}x & y\\0 & 62\\1 & 60.14\\2 & 58.3358\\3 & 56.5857\\4 & 54.8881\\5 & 53.2414\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx%20%26%20y%5C%5C0%20%26%2062%5C%5C1%20%26%2060.14%5C%5C2%20%26%2058.3358%5C%5C3%20%26%2056.5857%5C%5C4%20%26%2054.8881%5C%5C5%20%26%2053.2414%5Cend%7Barray%7D%5Cright%5D)
This is an exponential function because it has a constant ratio.
From our values, we can conclude that the equation is:

In five months, the stock will be $53.2414
<h2>
5. Write the exponential function</h2>
We are given two points:

We know that the exponential function is given by the form:

So:
![\bullet \ If \ x=0 \ then \ y=5 \\ \\ 5=ab^{0} \therefore a=5 \\ \\ \\ \bullet \ If \ x=3 \ y=135 \\ \\ 135=ab^{3} \therefore ab^{3}=135 \\ \\ \\ Finding \ b: \\ \\ \frac{ab^{3}}{a}=\frac{135}{5} \\ \\ b^3=27 \therefore b=\sqrt[3]{27} \therefore \boxed{b=3}](https://tex.z-dn.net/?f=%5Cbullet%20%5C%20If%20%5C%20x%3D0%20%5C%20then%20%5C%20y%3D5%20%5C%5C%20%5C%5C%205%3Dab%5E%7B0%7D%20%5Ctherefore%20a%3D5%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cbullet%20%5C%20If%20%5C%20x%3D3%20%5C%20y%3D135%20%5C%5C%20%5C%5C%20135%3Dab%5E%7B3%7D%20%5Ctherefore%20ab%5E%7B3%7D%3D135%20%5C%5C%20%5C%5C%20%5C%5C%20Finding%20%5C%20b%3A%20%5C%5C%20%5C%5C%20%5Cfrac%7Bab%5E%7B3%7D%7D%7Ba%7D%3D%5Cfrac%7B135%7D%7B5%7D%20%5C%5C%20%5C%5C%20b%5E3%3D27%20%5Ctherefore%20b%3D%5Csqrt%5B3%5D%7B27%7D%20%5Ctherefore%20%5Cboxed%7Bb%3D3%7D)
Then:

<h2>
6. Slope, length and midpoint</h2>
Here we are given two points:

So, the slope can be found as:

Using the distance formula we can find the length:

To find the midpoint, we have to use the midpoint formula:
