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.

step 2 of 2: how many protozoa are present after 2 days? 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.

step 2 of 2: how many protozoa are present after 2 days? 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" ] } ## Convert time to hours $$ t = 2 \text{ days} \times 24 \text{ hours/day} = 48 \text{ hours} $$ ## Evaluate the polynomial function $$ \begin{aligned} p(48) &= 0.05(48)^4 + 0.7(48)^3 + 3(48)^2 \ &= 0.05(5,308,416) + 0.7(110,592) + 3(2,304) \ &= 265,420.8 + 77,414.4 + 6,912 \ &= 349,747.2 \end{aligned} $$ ## Round to the nearest whole number $$ p(48) \approx 349,747 $$ How many protozoa are present after 2 days? Round your answer to the nearest whole number. 349,747 after 2 days (48 hours) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Applications" ] }

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Question

Explanation:

Convert time to hours

Evaluate the polynomial function

Round to the nearest whole number

Answer: