The task is to find the **ratio of the output values** that correspond to increases of 1 in the input value. (Note: Some authors call this a 1-unit growth/decay factor.)### Explanation of the Graph:The graph is a curve plotted on a coordinate plane with labeled points and axes. - The horizontal axis is labeled as $ x $ and the vertical axis is unmarked but typically represents $ y $.- The curve is shown descending from left to right.- Several points are marked on the graph: - $ (-1, 4) $ at $ x = -1 $ with $ y = 4 $. - $ (0, 1) $ at $ x = 0 $ with $ y = 1 $. - $ (1, 0.25) $ at $ x = 1 $ with $ y = 0.25 $.### Analyzing the Curve:- The curve suggests an exponential decay, where as $ x $ increases, $ y $ decreases rapidly.- The ratio of output values for a change in the input by 1 unit can be calculated between the marked points: - From $ x = -1 $ to $ x = 0 $: Ratio = $ \frac{y(0)}{y(-1)} = \frac{1}{4} $ - From $ x = 0 $ to $ x = 1 $: Ratio = $ \frac{y(1)}{y(0)} = \frac{0.25}{1} = 0.25 $This data suggests the graph represents an exponential function characterized by continuously halving for each increase in $ x $ by 1 unit.

According to the graph: Input and output values are: Input value Output Value -1…

Find the ratio of the output values that correspond to increases of 1 in the input value. (Note: Some authors call this a 1 - unit growth/decay factor.) 6- (-1, 4) 2+ 1 (0, 1) (1, 0.25) -2 -1 3 4 LO 3.

Find the ratio of the output values that correspond to increases of 1 in the input value. (Note: Some authors call this a 1 - unit growth/decay factor.) 6- (-1, 4) 2+ 1 (0, 1) (1, 0.25) -2 -1 3 4 LO 3.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

The task is to find the **ratio of the output values** that correspond to increases of 1 in the input value. (Note: Some authors call this a 1-unit growth/decay factor.)

### Explanation of the Graph:

The graph is a curve plotted on a coordinate plane with labeled points and axes.

- The horizontal axis is labeled as $ x $ and the vertical axis is unmarked but typically represents $ y $.
- The curve is shown descending from left to right.
- Several points are marked on the graph:
- $ (-1, 4) $ at $ x = -1 $ with $ y = 4 $.
- $ (0, 1) $ at $ x = 0 $ with $ y = 1 $.
- $ (1, 0.25) $ at $ x = 1 $ with $ y = 0.25 $.

### Analyzing the Curve:

- The curve suggests an exponential decay, where as $ x $ increases, $ y $ decreases rapidly.
- The ratio of output values for a change in the input by 1 unit can be calculated between the marked points:
- From $ x = -1 $ to $ x = 0 $: Ratio = $ \frac{y(0)}{y(-1)} = \frac{1}{4} $
- From $ x = 0 $ to $ x = 1 $: Ratio = $ \frac{y(1)}{y(0)} = \frac{0.25}{1} = 0.25 $

This data suggests the graph represents an exponential function characterized by continuously halving for each increase in $ x $ by 1 unit.

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