the estimated number of organisms in a population after $t$ days is shown in the table below.

which equation best models the situation?

- $t = 1.2(600)^n$
- $n = 600(1.2)^t$
- $n = 1.2(600)^t$
- $t = 600(1.2)^n$

Question

the estimated number of organisms in a population after $t$ days is shown in the table below.

which equation best models the situation?

- $t = 1.2(600)^n$
- $n = 600(1.2)^t$
- $n = 1.2(600)^t$
- $t = 600(1.2)^n$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Growth", "Exponential Modeling" ], "new_concepts": [], "current_concepts": [ "Exponential Growth", "Exponential Modeling" ] } ## Identify variables and model structure $$ \begin{aligned} &\text{Independent variable: } t \text{ (days)} \ &\text{Dependent variable: } n \text{ (estimated number of organisms)} \ &\text{General exponential model: } n = a(b)^t \end{aligned} $$ ## Test the model options with given data points $$ \begin{aligned} &\text{For } n = 600(1.2)^t: \ &t = 2 \implies n = 600(1.2)^2 = 600(1.44) = 864 \approx 860 \ &t = 4 \implies n = 600(1.2)^4 = 600(2.0736) = 1244.16 \approx 1250 \ &t = 6 \implies n = 600(1.2)^6 = 600(2.985984) = 1791.59 \approx 1800 \ &t = 8 \implies n = 600(1.2)^8 = 600(4.299817) = 2579.89 \approx 2600 \ &t = 10 \implies n = 600(1.2)^{10} = 600(6.191736) = 3715.04 \approx 3720 \end{aligned} $$ ## Compare with other options $$ \begin{aligned} &n = 1.2(600)^t \implies t=2 \implies n = 1.2(360000) = 432000 \quad (\text{Incorrect}) \ &t = 1.2(600)^n \text{ and } t = 600(1.2)^n \quad (\text{Incorrect independent/dependent variables}) \end{aligned} $$

(A) $t = 1.2(600)^n$

(B) $n = 600(1.2)^t$

(C) $n = 1.2(600)^t$

(D) $t = 600(1.2)^n$

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

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QUESTION IMAGE

Question

Explanation:

Identify variables and model structure

Test the model options with given data points

Compare with other options

Answer: