Math Problem Statement
Solution
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Here’s a quick recap:
- The function represents exponential decay.
- The completed table is:
-2 | 16 |
-1 | 4 |
0 | 1 |
1 | 0.25 |
- You should plot at least two points from the table (e.g., (-1,4) and (0,1)) and then sketch a smooth curve that decreases towards zero as increases.
Would you like a step-by-step guide on how to plot the function?
Related Questions:
- How do you determine if a function is exponential growth or decay?
- What happens to the function if we change the base from to ?
- How does the function behave for very large and very small values of ?
- What is the y-intercept of ?
- How can we rewrite using base 2?
Tip: The function never reaches zero—it only gets closer and closer, forming a horizontal asymptote at .
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Graphing
Exponential Decay
Formulas
y = a^x where 0 < a < 1 represents exponential decay
Theorems
Exponential functions have a horizontal asymptote at y = 0 for decay
Suitable Grade Level
Grades 8-10
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