Math Problem Statement
Indicate whether the function models exponential growth or exponential decay based on the provided equations.
Solution
Let’s analyze the equations to determine whether they represent exponential growth or decay.
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:
- The exponent has a positive coefficient (0.143), so the function represents exponential growth.
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- The base , indicating the function represents exponential growth.
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- The base , so this function also represents exponential growth.
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:
- The exponent has a negative coefficient (-1.58), so this function represents exponential decay.
Would you like further clarification or details? Here are some related questions to consider:
- What is the general formula for exponential growth and decay?
- How do you determine the growth or decay factor in a function?
- Can a base between 0 and 1 represent exponential growth?
- What real-world examples can model exponential growth or decay?
- How does changing the coefficient in front of the exponential term affect the graph of the function?
Tip: Always check the sign of the exponent or the value of the base to identify growth or decay.
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Growth and Decay Analysis
Formulas
y = Ce^(kt) where k > 0 indicates growth and k < 0 indicates decay
y = Cb^t where b > 1 indicates growth and 0 < b < 1 indicates decay
Theorems
Exponential Growth and Decay Rules
Suitable Grade Level
Grades 9-12