what is the rate of change of the function described in the table?

$\frac{12}{5}$

$5$

$\frac{25}{2}$

$25$

Question

what is the rate of change of the function described in the table?

$\frac{12}{5}$

$5$

$\frac{25}{2}$

$25$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Average Rate of Change" ], "new_concepts": [], "current_concepts": [ "Average Rate of Change", "Exponential Growth Model" ] } ## Identify the function type and constant ratio $$ \begin{aligned} &\text{Let } y = f(x) = a \cdot b^x\ &\frac{f(1)}{f(0)} = \frac{5/2}{1/2} = 5\ &\frac{f(2)}{f(1)} = \frac{25/2}{5/2} = 5\ &\frac{f(3)}{f(2)} = \frac{125/2}{25/2} = 5\ &b = 5,\quad a = f(0) = \frac{1}{2}\ &f(x) = \frac{1}{2} \cdot 5^x \end{aligned} $$ ## Determine the rate of change $$ \begin{aligned} &\text{Rate of change (growth factor) } = 5 \end{aligned} $$

(A) $\frac{12}{5}$

(B) 5

(C) $\frac{25}{2}$

(D) 25

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Average Rate of Change" ] }

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Question

Explanation:

Identify the function type and constant ratio

Determine the rate of change

Answer: