an invasive plant species spreads rapidly in a new environment. the number of plants triples every month. suppose there are initially 4 plants.

what is an explicit equation that can be used to find the number of plants after $n$ months?

$a_n = 3 \cdot 4^{(n-1)}$
$a_n = 4 \cdot 3^{(n)}$
$a_n = 4 \cdot 3^{(n-1)}$
$a_n = 3 \cdot 4^{(n+1)}$

Question

an invasive plant species spreads rapidly in a new environment. the number of plants triples every month. suppose there are initially 4 plants.

what is an explicit equation that can be used to find the number of plants after $n$ months?

$a_n = 3 \cdot 4^{(n-1)}$
$a_n = 4 \cdot 3^{(n)}$
$a_n = 4 \cdot 3^{(n-1)}$
$a_n = 3 \cdot 4^{(n+1)}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Modeling", "Growth Factor" ], "new_concepts": [ "Geometric Sequences", "Explicit Equations" ], "current_concepts": [ "Exponential Modeling", "Growth Factor", "Geometric Sequences", "Explicit Equations" ] } ## Identify the initial value and growth factor $$ \begin{aligned} &\text{Initial value } (a_0) = 4\ &\text{Growth factor } (b) = 3 \end{aligned} $$ ## Formulate the explicit equation $$ a_n = 4 \cdot 3^n $$ ## Match with the given options $$ a_n = 4 \cdot 3^{(n)} $$

(A) $a_n = 3 \cdot 4^{(n-1)}$

(B) $a_n = 4 \cdot 3^{(n)}$

(C) $a_n = 4 \cdot 3^{(n-1)}$

(D) $a_n = 3 \cdot 4^{(n+1)}$

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

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Question

Explanation:

Identify the initial value and growth factor

Formulate the explicit equation

Match with the given options

Answer: