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

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Functions" ], "new_concepts": [], "current_concepts": [ "Exponential Functions", "Growth Factor" ] } ## 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 $$ \text{Growth Factor} = b = 15 $$

(A) $\frac{1}{5}$

(B) $\frac{1}{3}$

(C) 5

(D) 15

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Functions" ] }

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Question

Explanation:

Identify the standard form of an exponential function

Match the given function to the standard form

Determine the growth factor

Answer: