select the correct answer.

a populations instantaneous growth rate is the rate at which it grows for every instant in time. function $r$ gives the instantaneous growth rate of a bacterial culture $x$ hours after the start of an experiment.

\
(x) = 0.01(x + 2)(x^2 - 9)\

how many hours after the experiment began was the instantaneous growth rate equal to 0?

* 0
* 9
* 2
* 3

Question

select the correct answer.

a populations instantaneous growth rate is the rate at which it grows for every instant in time. function $r$ gives the instantaneous growth rate of a bacterial culture $x$ hours after the start of an experiment.

\
(x) = 0.01(x + 2)(x^2 - 9)\

how many hours after the experiment began was the instantaneous growth rate equal to 0?

* 0
* 9
* 2
* 3

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Zeros and Factors", "Viable Solutions in Context" ], "new_concepts": [], "current_concepts": [ "Zeros and Factors", "Viable Solutions in Context", "Polynomial Factoring" ] } ## Set the growth rate function equal to zero $$ 0.01(x + 2)(x^2 - 9) = 0 $$ ## Solve for the roots of the polynomial $$ \begin{aligned} x + 2 = 0 &\implies x = -2 \ x^2 - 9 = 0 &\implies x^2 = 9 \implies x = \pm 3 \end{aligned} $$ ## Determine the viable solution in context $$ \begin{aligned} &\text{Since } x \ge 0 \text{ represents the hours after the experiment began:} \ &x = -2 \quad (\text{invalid}) \ &x = -3 \quad (\text{invalid}) \ &x = 3 \quad (\text{valid}) \end{aligned} $$

0

9

2

3

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Zeros and Factors" ] }

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QUESTION IMAGE

Question

Explanation:

Set the growth rate function equal to zero

Solve for the roots of the polynomial

Determine the viable solution in context

Answer: