Math Problem Statement
Which graph represents the exponential decay function in the table below?
Solution
The given table represents an exponential decay function, as the values of decrease as increases:
x & y \\ \hline -2 & 32 \\ -1 & 16 \\ 0 & 8 \\ 1 & 4 \\ 3 & 2 \\ \end{array}$$ Observing the pattern, the function follows: $$y = 8 \times \left(\frac{1}{2}\right)^x$$ Now, looking at the graphs: 1. **Exponential decay graphs** decrease from left to right. 2. **Exponential growth graphs** increase from left to right. From the images, the **correct graph** should be one that decreases as $$x$$ increases. The correct answer is the **graph with the decreasing curve**, which appears to be in the **first option in both images**. Would you like a step-by-step verification of the function? ### Related Questions: 1. How do you determine if a function represents exponential decay or growth? 2. What is the general formula for an exponential decay function? 3. How can you calculate the decay rate from a table of values? 4. How do transformations affect exponential decay functions? 5. What real-world applications use exponential decay? #### Tip: In an **exponential decay** function $$y = a \cdot b^x$$, the base $$b$$ is always between 0 and 1 (e.g., $$0 < b < 1$$).Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Exponential Decay
Tables of Values
Graphing Functions
Formulas
y = a * b^x (Exponential Function)
Theorems
Exponential decay functions decrease as x increases, where the base b is between 0 and 1.
Suitable Grade Level
Grades 7-9
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