The terms shown below are the first three terms of a geometric sequence whose common ratio is positive.
1 answer:
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Answer:
See Explanation.
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
Slope Formula:
Slope-Intercept Form: y = mx + b
- m - slope
- b - y-intercept
Linear Regression
Step-by-step explanation:
We can draw any best line of fit, as long as it is <em>reasonable</em> around the points that are given.
We can just take 2 points and use slope formula and Slope-Intercept Form to find the equation for the best line of fit.
Using Linear Regression, we can determine the <em>true</em> best line of fit using graphing utilities.
<u>Finding the best line of fit</u>
<em>Define 2 points</em>
Point (21600, 205)
Point (27000, 290)
<em>Find slope m</em>
- Substitute in point [SF]:
- [Fraction] Subtract:
- [Fraction] Simplify:
<em>Find equation</em>
- Define equation [SIF]:
- Substitute in point:
- Multiply:
- Isolate y-intercept <em>b</em>:
- Rewrite:
- Redefine equation:
Slope-Intercept Form tells us that our slope <em>m</em> = and our y-intercept
.
Setting this as function f(x), we can see from the graph that it is extremely accurate (Blue line).
<u>Using Linear Regression</u>
Depending on the graphing calc you have, the steps may be different.
Using a graphing calc, we can use statistics and determine the <em>best</em> best line of fit.
When we determine the values, we should see that our equation would be g(x) (Green Line).
<em>Credit to Lauren for collabing w/ me in graphing.</em>
