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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Question
Find the equation of the exponential function whose graph is shown below
f(x)=

Transcribed Image Text:Title: Determining the Equation of an Exponential Function
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**Question:**
Find the equation of the exponential function whose graph is shown below.
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**Graph Description:**
The graph depicts an exponential function, which is represented by a smooth curve. Key observations from the graph include:
- **Axes:** The horizontal axis is labeled as the x-axis, ranging from -2 to 3, and the vertical axis is labeled as the y-axis, ranging from 0 to 16.
- **Curve Behavior:**
- As x moves from -2 towards 0, the curve gradually increases in value.
- From x = 0 onward, the curve rises steeply, indicating rapid growth.
- **Specific Points:**
- At x = 0, the y-value is 1.
- At x = 1, the y-value is around 2.
- At x = 2, the y-value is between 4 and 8.
This type of curve is typical for exponential functions of the form \( y = a \cdot b^x \), where:
- \( a \) is the initial value or the y-intercept of the function.
- \( b \) is the base of the exponential function that dictates the rate of growth or decay.
Given the observations, you are tasked with identifying the equation that accurately represents the graph.
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**Discussion:**
To find the exact equation, one could use known points along the curve. For example, since at x = 0, y = 1, we can state that \( a \cdot b^0 = 1 \Rightarrow a = 1 \).
The rapid increase in y-values as x increases suggests an exponential growth, typically represented when \( b > 1 \). Further calculations can determine the precise value of \( b \).
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Feel free to explore more on identifying and solving exponential functions through graph analysis in the detailed lessons available on our website.
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