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Katen [24]
3 years ago
13

I need help with 4 5 and 6

Mathematics
1 answer:
Akimi4 [234]3 years ago
7 0
<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 x=0 the first month then:

at \ x=0 \ y=62 \\ \\ at \ x=1 \ y=62-62\times 3\%=60.14 \\ \\ at \ x=2 \ y=60.14-60.14\times 3\%=58.3358 \\ \\ at \ x=3 \ y=58.3358-58.3358\times 3\%=56.5857 \\ \\ at \ x=4 \ y=56.5857-56.5857\times 3\%=54.8881 \\ \\ at \ x=5 \ y=54.8881-54.8881\times 3\%=53.2414

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]

This is an exponential function because it has a constant ratio.

From our values, we can conclude that the equation is:

y=62(100%-3%)^{x} \\ \\ \boxed{y=62(0.97)^{x}}

In five months, the stock will be $53.2414

<h2>5. Write the exponential function</h2>

We are given two points:

P_{1}(0,5) \\ \\ P_{2}(3,135)

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

y=ab^{x}

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}

Then:

\boxed{y=5(3)^{x}}

<h2>6. Slope, length and midpoint</h2>

Here we are given two points:

A(4,9) \ and \ B(-2,3)

So, the slope can be found as:

m=\frac{Change \ in \ y}{Change \ in \ x} \\ \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ m=\frac{3-9}{-2-4} \\ \\ \boxed{m=1}

Using the distance formula we can find the length:

d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2} \\ \\ d=\sqrt{(-2-4)^2+(3-9)^2} \\ \\ d=\sqrt{36+36} \\ \\ d=\sqrt{72} \\ \\ \boxed{d=6\sqrt{2}}

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

Midpoint=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}) \\ \\ Midpoint=(\frac{4-2}{2},\frac{9+3}{2}) \\ \\ \boxed{Midpoint=(1,6)}

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