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.

  1. y=237e0.143ty = 237e^{0.143t}:

    • The exponent 0.143t0.143t has a positive coefficient (0.143), so the function represents exponential growth.
  2. y=1731.92ty = 173 \cdot 1.92^t:

    • The base 1.92>11.92 > 1, indicating the function represents exponential growth.
  3. y=247(1.5)ty = 247 \cdot (1.5)^t:

    • The base 1.5>11.5 > 1, so this function also represents exponential growth.
  4. y=97e1.58ty = 97e^{-1.58t}:

    • The exponent 1.58t-1.58t 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:

  1. What is the general formula for exponential growth and decay?
  2. How do you determine the growth or decay factor in a function?
  3. Can a base between 0 and 1 represent exponential growth?
  4. What real-world examples can model exponential growth or decay?
  5. 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