Math Problem Statement

Which of the following equations represents exponential growth? Type the correct equation in the space provided. y = y = 0 . 1x y = 1 . 5x y = (1 . 5) x y = (0 . 1) x

Solution

The equation that represents exponential growth is:

y=(1.5)xy = (1.5)^x

In this equation, the base (1.5) is greater than 1, which indicates exponential growth. The variable xx is the exponent, and the function increases as xx increases.

Relative Questions:

  1. What is the difference between exponential growth and exponential decay?
  2. How do you determine if an exponential function represents growth or decay?
  3. What are some real-world examples of exponential growth?
  4. How does the value of the base in an exponential function affect the rate of growth?
  5. What happens to an exponential function if the base is less than 1 but greater than 0?

Tip: Exponential growth functions always have a base greater than 1, leading to faster increases as the variable increases.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponential Functions
Exponential Growth and Decay

Formulas

Exponential Growth: y = a * b^x where b > 1
Exponential Decay: y = a * b^x where 0 < b < 1

Theorems

Exponential Growth Theorem

Suitable Grade Level

Grades 8-10