The equation that models the exponential decline is y = 46348587109809610(0.9861)ˣ if the population over the past 20 years is provided.
<h3>What is the line of best fit?</h3>
A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
Let's suppose the equation that models the exponential decline is:
From the data given, we can calculate the value of a and b:
a = 46348587109809610
b = 0.9861
y = 46348587109809610(0.9861)ˣ
Thus, the equation that models the exponential decline is y = 46348587109809610(0.9861)ˣ if the population over the past 20 years is provided.
Learn more about the line of best fit here:
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11x + 2 is combining like terms
The answer is 70/100ths i am pretty sure
Solution:
Since the graph passes through the given points, (7, 20) & (-2, 11) are the solutions of the given equation <em>y = x + ?</em>.
⇒<em>(x, y)</em> = (7, 20); (-2, 11)
Substituting the variables with (7, 20),
20 = 7 + <em>?</em>
20 - 7 = <em>?</em>
<em>?</em> = 13
Similarly,
11 = -2 + <em>?</em>
<em>?</em> = 13
∴ <em>y</em> = 13
To find the equation of the graph, what we do is to recognize some characteristics of a sine function:
- Amplitude: The amplitude of the sine function is the distance from the middle value or line running through the graph up to the highest point. In this case, the amplitude is 1.
- Period: The period of a sine function is defined as the length of one complete sine wave or one complete cycle of the curve. It can be found using the equation: P=2pi/B.
Why are these characteristics important?
Because the sine function has the following general form:
In this problem, we have A=1 and we know that the period equals 2pi/3. So,
Therefore, the equation of the graph is:
