Math Problem Statement

y=182x2^1.4t linear relationship

Solution

The given equation is:

y=182x21.4ty = 182x 2^{1.4t}

This equation represents an exponential relationship because the variable tt 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:

  1. Original equation: y=182x21.4ty = 182x 2^{1.4t}

  2. Take the natural logarithm (ln\ln) of both sides: ln(y)=ln(182x21.4t)\ln(y) = \ln(182x 2^{1.4t})

  3. 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