Math Problem Statement

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Solution

The problem asks for the equation that matches the graph shown in the image.

Analysis of the Graph:

The graph appears to be a reflection and vertical shift of a basic exponential function. The curve has the following features:

  • It is decreasing, suggesting that the base of the exponent is between 0 and 1.
  • The curve approaches the horizontal axis (x-axis) asymptotically from above.
  • It intersects the y-axis at a point below the origin.

Step-by-Step Approach:

Given that the graph is decreasing, we're looking for an equation that has a form similar to y=abx+cy = a \cdot b^x + c, where 0<b<10 < b < 1 and aa and cc adjust the shape and position.

Let's now check the equations provided in the options:

  1. Option A: y=(2)312y = -(2) \cdot 3^1 - 2
    This is a linear equation, not exponential. The graph will be a straight line, which does not match.

  2. **Option B: (

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Graph Analysis
Reflections and Transformations

Formulas

Exponential function formula y = a * b^x + c

Theorems

Properties of Exponential Functions

Suitable Grade Level

Grades 10-12