which statements correctly describe how the graph of the geometric sequence below should appear?

(640, 160, 40, 10, \dots)

select two options.

the graph will show exponential growth.
the graph will appear linear.
the domain will be the set of natural numbers.
the range will be the set of natural numbers.
the graph will show exponential decay.

Question

which statements correctly describe how the graph of the geometric sequence below should appear?

(640, 160, 40, 10, \dots)

select two options.

the graph will show exponential growth.
  the graph will appear linear.
  the domain will be the set of natural numbers.
  the range will be the set of natural numbers.
  the graph will show exponential decay.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Sequences", "Exponential Decay", "Domain and Range" ], "new_concepts": [], "current_concepts": [ "Geometric Sequences", "Exponential Decay", "Domain and Range" ] } ## Analyze the geometric sequence terms $$ \begin{aligned} &a_1 = 640 \ &a_2 = 160 \ &a_3 = 40 \ &a_4 = 10 \ &r = \frac{160}{640} = \frac{1}{4} = 0.25 \end{aligned} $$ ## Determine the behavior of the graph $$ \begin{aligned} &a_n = 640 \cdot (0.25)^{n-1} \ &0 < r < 1 \implies \text{Exponential decay} \end{aligned} $$ ## Identify the domain of the sequence $$ \begin{aligned} &\text{Domain} = \{1, 2, 3, 4, \dots\} = \mathbb{N} \quad (\text{Set of natural numbers}) \ &\text{Range} = \{640, 160, 40, 10, \dots\} eq \mathbb{N} \end{aligned} $$

The graph will show exponential growth

The graph will appear linear.

The domain will be the set of natural numbers.

The range will be the set of natural numbers.

The graph will show exponential decay.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Geometric Sequences" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Analyze the geometric sequence terms

Determine the behavior of the graph

Identify the domain of the sequence

Answer: