f(x) = 100(0.7)x is a mathematical expression used to represent a linear function, which is a function that produces a straight line when graphed. This article will explain what this expression means and how to read the graph of f(x) = 100(0.7)x.
What is f(x) = 100(0.7)x?
f(x) = 100(0.7)x is an equation that describes a linear function. It is made up of two parts: f(x) and 100(0.7)x. f(x) is a function, and 100(0.7)x is an expression that describes the slope of the line. The slope of a line is the amount it rises or falls between any two points.
In this equation, the number 100 is the y-intercept, or the point where the line crosses the y-axis. The number 0.7 is the slope of the line. It tells us how much the line rises or falls for every unit increase in x.
Understanding the Graph of f(x) = 100(0.7)x
The graph of f(x) = 100(0.7)x is a straight line that passes through the point (0, 100) and has a slope of 0.7. The y-intercept is 100, meaning that the line crosses the y-axis at the point (0, 100).
The slope of the line tells us that for every unit increase in x, the line rises or falls by 0.7 units. This means that for every unit increase in x, the y-value increases by 0.7 units. For instance, if x increases from 1 to 2, the corresponding y-value will increase from 107 to 114.
In conclusion, f(x) = 100(0.7)x is an equation that describes a linear function with a y-intercept of 100 and a slope of 0.7. The graph of this equation is a straight line that passes through the point (0, 100) and has a slope of 0.7. Understanding this equation and its graph can be helpful when solving linear equations.
