Math Problem Statement
y=182x2^1.4t linear relationship
Solution
The given equation is:
This equation represents an exponential relationship because the variable is in the exponent. To find a linear relationship, we typically linearize the equation, which can be done by taking the logarithm of both sides.
Step-by-Step Process to Linearize:
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Original equation:
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Take the natural logarithm () of both sides:
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Use the logarithmic properties:
- ( \ln(a \cdot b)
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Logarithms
Linearization
Formulas
y = 182x 2^{1.4t}
logarithmic property: ln(ab) = ln(a) + ln(b)
linearization via logarithms: ln(y) = ln(182x) + 1.4t ln(2)
Theorems
Properties of Logarithms
Exponential Growth and Decay
Suitable Grade Level
Grades 10-12
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