the number of protozoa in a biology laboratory experiment is given by the polynomial function $p(t) = 0.02t^4 + 0.4t^3 + 6t^2$, where $p$ is the number of protozoa after $t$ hours.

step 1 of 2: determine the number of protozoa after 5 hours. round your answer to the nearest whole number.

Question

the number of protozoa in a biology laboratory experiment is given by the polynomial function $p(t) = 0.02t^4 + 0.4t^3 + 6t^2$, where $p$ is the number of protozoa after $t$ hours.

step 1 of 2: determine the number of protozoa after 5 hours. round your answer to the nearest whole number.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Evaluation", "Polynomial Applications" ], "new_concepts": [], "current_concepts": [ "Function Evaluation", "Polynomial Applications" ] } ## Substitute t = 5 into the polynomial function $$ p(5) = 0.02(5)^4 + 0.4(5)^3 + 6(5)^2 $$ ## Calculate each term $$ \begin{aligned} 0.02(5)^4 &= 0.02 \times 625 = 12.5 \ 0.4(5)^3 &= 0.4 \times 125 = 50 \ 6(5)^2 &= 6 \times 25 = 150 \end{aligned} $$ ## Sum the terms and round to the nearest whole number $$ \begin{aligned} p(5) &= 12.5 + 50 + 150 = 212.5 \ p(5) &\approx 213 \end{aligned} $$ Determine the number of protozoa after 5 hours. Round your answer to the nearest whole number. 213 protozoa after 5 hours { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Evaluation" ] }

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QUESTION IMAGE

Question

Explanation:

Substitute t = 5 into the polynomial function

Calculate each term

Sum the terms and round to the nearest whole number

Answer: