Math Problem Statement

y=(e)^(x/2)

Solution

You have the equation:

y=ex2y = e^{\frac{x}{2}}

This is an exponential function where ee is the base of the natural logarithm, approximately equal to 2.71828, and xx is the variable.

Would you like to know something specific about this function, such as its graph, its derivative, or its behavior for certain values of xx?


Here are a few follow-up questions related to this topic:

  1. What is the derivative of y=ex2y = e^{\frac{x}{2}}?
  2. How would you graph the function y=ex2y = e^{\frac{x}{2}}?
  3. What is the behavior of y=ex2y = e^{\frac{x}{2}} as xx approaches infinity?
  4. How do you solve for xx if given a specific value for yy?
  5. What happens if the function was y=ex/3y = e^{x/3} instead?

Tip: Exponential functions of the form y=ekxy = e^{kx} have the property that their rate of change (slope) is proportional to their current value, meaning the graph will always be increasing for positive values of kk.

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Differentiation
Graphing

Formulas

y = e^(x/2)
dy/dx = (1/2) * e^(x/2)

Theorems

Derivative of Exponential Functions
Properties of Exponential Growth

Suitable Grade Level

Grades 10-12