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

$ \bigcirc \frac{12}{5} $
$ \bigcirc 5 $
$ \bigcirc \frac{25}{2} $
$ \bigcirc 25 $

Question

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

$ \bigcirc \frac{12}{5} $
$ \bigcirc 5 $
$ \bigcirc \frac{25}{2} $
$ \bigcirc 25 $

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": [ "Common Ratio" ], "current_concepts": [ "Exponential Functions", "Common Ratio" ] } ## Identify the function type from the table $$ \begin{aligned} &x = -1 \implies y = \frac{1}{10} \ &x = 0 \implies y = \frac{1}{2} \ &x = 1 \implies y = \frac{5}{2} \ &x = 2 \implies y = \frac{25}{2} \ &x = 3 \implies y = \frac{125}{2} \end{aligned} $$ ## Calculate the constant ratio between successive terms $$ \begin{aligned} r &= \frac{y(0)}{y(-1)} = \frac{\frac{1}{2}}{\frac{1}{10}} = 5 \ r &= \frac{y(1)}{y(0)} = \frac{\frac{5}{2}}{\frac{1}{2}} = 5 \ r &= \frac{y(2)}{y(1)} = \frac{\frac{25}{2}}{\frac{5}{2}} = 5 \ r &= \frac{y(3)}{y(2)} = \frac{\frac{125}{2}}{\frac{25}{2}} = 5 \end{aligned} $$ ## Determine the rate of change (growth factor) $$ \begin{aligned} y(x) &= a \cdot b^x \ y(0) &= a = \frac{1}{2} \ b &= 5 \end{aligned} $$

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

(B) 5

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

(D) 25

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

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QUESTION IMAGE

Question

Explanation:

Identify the function type from the table

Calculate the constant ratio between successive terms

Determine the rate of change (growth factor)

Answer: