the number of protozoa in a biology laboratory experiment is given by the polynomial function $p(t) = 0.05t^4 + 0.7t^3 + 3t^2$, where $p$ is the number of protozoa after $t$ hours.

determine the number of protozoa after 8 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 $p(t) = 0.05t^4 + 0.7t^3 + 3t^2$, where $p$ is the number of protozoa after $t$ hours.

determine the number of protozoa after 8 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" ], "new_concepts": [ "Polynomial Applications" ], "current_concepts": [ "Function Evaluation", "Polynomial Applications" ] } ## Substitute t = 8 into the polynomial function $$ p(8) = 0.05(8)^4 + 0.7(8)^3 + 3(8)^2 $$ ## Calculate each term $$ \begin{aligned} 0.05(4096) &= 204.8 \ 0.7(512) &= 358.4 \ 3(64) &= 192 \end{aligned} $$ ## Sum the terms and round to the nearest whole number $$ \begin{aligned} p(8) &= 204.8 + 358.4 + 192 \ p(8) &= 755.2 \ p(8) &\approx 755 \end{aligned} $$ Determine the number of protozoa after 8 hours. Round your answer to the nearest whole number. 755 protozoa after 8 hours { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Evaluation" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Substitute t = 8 into the polynomial function

Calculate each term

Sum the terms and round to the nearest whole number

Answer: