Let's analyze the given equation:

$y = 16(0.5)^x$

This represents an exponential function where:

• The initial value (when $x = 0$) is $y = 16$.
• The base of the exponential function is $0.5$, which means the function is decreasing (since $0.5 < 1$).

To determine which statement about the graph is NOT true, we need to consider the following characteristics of exponential graphs:

1. Exponential Growth/Decay: Since $0.5 < 1$, the function represents exponential decay, meaning the graph will decrease as $x$ increases.
2. Y-intercept: The graph crosses the y-axis at $y = 16$ when $x = 0$.
3. Horizontal Asymptote: The graph will approach but never touch the line $y = 0$ as $x \to \infty$. This is the horizontal asymptote.
4. Shape: The graph will start high at $y = 16$ when $x = 0$ and decrease as $x$ increases. It will be a decreasing curve.

Example statements that could be true or false:

• "The graph will have a horizontal asymptote at $y = 0$." (True)
• "The graph increases as $x$ increases." (False, because the base is less than 1, causing decay.)
• "The graph crosses the y-axis at $y = 16$." (True)
• "The graph will approach zero but never touch the x-axis." (True)
• "The graph represents exponential growth." (False, it represents exponential decay.)

Thus, a statement like "The graph increases as $x$ increases" would be NOT true, as the graph decreases instead.

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Would you like to dive deeper into any part of this? Here are some related questions:

1. What happens if the base of the exponential function is greater than 1?
2. How does the horizontal asymptote affect the behavior of the graph?
3. What is the effect of changing the coefficient $16$ in the equation?
4. How can we find the value of $y$ at different $x$-values for this function?
5. How can you graph this function using a table of values?

Tip: In an exponential decay function like this, the base being between 0 and 1 makes the graph decrease, while a base greater than 1 causes exponential growth.