9 9. What is the slope of the line y = 3x + 2?
1 answer:
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<span>First. <u>Finding the x-intercepts of </u>
</span><span>
Let be the change in water level. So to find the x-intercepts of this function we can use The Rational Zero Test that states:
To find the zeros of the polynomial:
We use the Trial-and-Error Method which states that a factor of the constant term:
can be a zero of a polynomial (the x-intercepts).
So let's use an example: Suppose you have the following polynomial:
where the constant term is
. The possible zeros are the factors of this term, that is:
.
Thus:
</span>
<span>
From the foregoing, we can affirm that
are zeros of the polynomial.
</span>Second. <u>Construction a rough graph of</u>
Given that this is a polynomial, then the function is continuous. To graph it we set the roots on the coordinate system. We take the interval:
![[-2,-1]](https://tex.z-dn.net/?f=%5B-2%2C-1%5D)
and compute
where 
is a real number between -2 and -1. If 
, the curve start rising, if not, the curve start falling. For instance:
Therefore the curve start falling and it goes up and down until
and from this point it rises without a bound as shown in the figure below
</span><span>
Let
To find the zeros of the polynomial:
We use the Trial-and-Error Method which states that a factor of the constant term:
can be a zero of a polynomial (the x-intercepts).
So let's use an example: Suppose you have the following polynomial:
where the constant term is
Thus:
</span>
From the foregoing, we can affirm that
</span>Second. <u>Construction a rough graph of</u>
Given that this is a polynomial, then the function is continuous. To graph it we set the roots on the coordinate system. We take the interval:
and compute
Therefore the curve start falling and it goes up and down until
Let value intially be = P
Then it is decreased by 20 %.
So 20% of P =
So after 1 year value is decreased by 0.2P
so value after 1 year will be = P - 0.2P (as its decreased so we will subtract 0.2P from original value P) = 0.8P-------------------------------------(1)
Similarly for 2nd year, this value 0.8P will again be decreased by 20 %
so 20% of 0.8P =
So after 2 years value is decreased by (0.2)(0.8P)
so value after 2 years will be = 0.8P - 0.2(0.8P)
taking 0.8P common out we get 0.8P(1-0.2)
= 0.8P(0.8)
-------------------------(2)
Similarly after 3 years, this value will again be decreased by 20 %
so 20% of
So after 3 years value is decreased by
so value after 3 years will be =
taking common out we get
-----------------------(3)
so from (1), (2), (3) we can see the following pattern
value after 1 year is P(0.8) or
value after 2 years is
value after 3 years is
so value after x years will be ( whatever is the year, that is raised to power on 0.8)
So function is best described by exponential model
where y is the value after x years
so thats the final answer