Question

consider the exponential function \\(f(x) = \frac{1}{5}(15^x)\\). what is the value of the growth factor of the function?

• \\(\frac{1}{5}\\)
• \\(\frac{1}{3}\\)
• 5
• 15

Explanation:

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<reasoning>

Identify the standard form of an exponential function

\[
f(x) = a \cdot b^x
\]

Match the given function to the standard form

\[
f(x) = \frac{1}{5}(15^x) \implies a = \frac{1}{5},\quad b = 15
\]

Determine the growth factor

\[
\text{Growth Factor} = b = 15
\]
</reasoning>

<answer>
<mcq-option>(A) \(\frac{1}{5}\)</mcq-option>
<mcq-option>(B) \(\frac{1}{3}\)</mcq-option>
<mcq-option>(C) 5</mcq-option>
<mcq-correct>(D) 15</mcq-correct>
</answer>

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Answer:

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<reasoning>

Identify the standard form of an exponential function

\[
f(x) = a \cdot b^x
\]

Match the given function to the standard form

\[
f(x) = \frac{1}{5}(15^x) \implies a = \frac{1}{5},\quad b = 15
\]

Determine the growth factor

\[
\text{Growth Factor} = b = 15
\]
</reasoning>

<answer>
<mcq-option>(A) \(\frac{1}{5}\)</mcq-option>
<mcq-option>(B) \(\frac{1}{3}\)</mcq-option>
<mcq-option>(C) 5</mcq-option>
<mcq-correct>(D) 15</mcq-correct>
</answer>

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