the function $f(x) = 2 \cdot 5^x$ can be used to represent the curve through the points $(1, 10)$, $(2, 50)$, and $(3, 250)$. what is the multiplicative rate of change of the function?

$\bigcirc$ 2
$\bigcirc$ 5
$\bigcirc$ 10
$\bigcirc$ 32

Question

the function $f(x) = 2 \cdot 5^x$ can be used to represent the curve through the points $(1, 10)$, $(2, 50)$, and $(3, 250)$. what is the multiplicative rate of change of the function?

$\bigcirc$ 2
$\bigcirc$ 5
$\bigcirc$ 10
$\bigcirc$ 32

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": [ "Multiplicative Rate of Change" ], "current_concepts": [ "Exponential Functions", "Multiplicative Rate of Change" ] } ## Identify the exponential function form $$ f(x) = a \cdot b^x = 2 \cdot 5^x $$ ## Determine the base of the exponential function $$ b = 5 $$ ## Relate the base to the multiplicative rate of change $$ \text{Multiplicative Rate of Change} = b = 5 $$

2

5

10

32

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

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QUESTION IMAGE

Question

Explanation:

Identify the exponential function form

Determine the base of the exponential function

Relate the base to the multiplicative rate of change

Answer: