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:
In this equation, the base (1.5) is greater than 1, which indicates exponential growth. The variable is the exponent, and the function increases as increases.
Relative Questions:
- What is the difference between exponential growth and exponential decay?
- How do you determine if an exponential function represents growth or decay?
- What are some real-world examples of exponential growth?
- How does the value of the base in an exponential function affect the rate of growth?
- 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