Questions: Describe the graph of the function y=2 * 4^x

Describe the graph of the function y=2 * 4^x
Transcript text: Describe the graph of the function $y=2 \cdot 4^{x}$
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Solution

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Solution Steps

To determine the nature of the graph of the function \( y = 2 \cdot 4^x \), we need to analyze the base of the exponential function. Since the base is greater than 1, the function represents exponential growth. The \( y \)-intercept can be found by evaluating the function at \( x = 0 \).

Step 1: Determine the Nature of the Function

The function is given by \( y = 2 \cdot 4^x \). Since the base of the exponential function, \( 4 \), is greater than \( 1 \), this indicates that the function represents exponential growth.

Step 2: Calculate the \( y \)-Intercept

To find the \( y \)-intercept, we evaluate the function at \( x = 0 \): \[ y(0) = 2 \cdot 4^0 = 2 \cdot 1 = 2 \] Thus, the \( y \)-intercept is \( 2 \).

Final Answer

The function \( y = 2 \cdot 4^x \) exhibits exponential growth with a \( y \)-intercept of \( 2 \). Therefore, the answer is \( \boxed{\text{Exponential growth, with a } y\text{-intercept of } 2} \).

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