**Grafica la función.**

\[f(x)=2\left(\dfrac{1}2\right)^x\]

Here is the graph of the function:

\[
f(x) = 2\left(\frac{1}{2}\right)^x
\]

This curve represents exponential decay since the base \( \frac{1}{2} < 1 \). The function decreases rapidly as \( x \) becomes more positive.

Would you like more details or have any questions?

Here are 8 related questions to explore:

1. How does the graph change if the coefficient 2 is increased or decreased?
2. What happens to the graph if the base \( \frac{1}{2} \) is replaced by a number greater than 1?
3. How can you determine the horizontal asymptote of this function?
4. How would the graph look if you reflected it across the y-axis?
5. What is the y-intercept of this function, and how is it calculated?
6. How does changing \( x \) in the exponent affect the steepness of the curve?
7. What are some real-life examples of exponential decay modeled by functions like this?
8. How does the rate of decay change if the base is smaller, like \( \frac{1}{3} \) instead of \( \frac{1}{2} \)?

**Tip:** Exponential decay functions have a base between 0 and 1, causing the graph to approach the x-axis as \( x \) increases.

Explore the graph of the exponential decay function f(x) = 2 * (1/2)^x. Understand its properties, including the rapid decrease as x increases and its base effect on decay rate. Suitable for Grades 10-12.

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