a scientist writes the equation $n(h) = 100e^{0.25h}$ to model the growth of a certain bacteria in a petri dish, where $n$ represents the number of bacteria after $h$ hours. after approximately how many hours will 450 bacteria be present? round your answer to the nearest whole number.

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Question

a scientist writes the equation $n(h) = 100e^{0.25h}$ to model the growth of a certain bacteria in a petri dish, where $n$ represents the number of bacteria after $h$ hours. after approximately how many hours will 450 bacteria be present? round your answer to the nearest whole number.

1 hour
6 hours
13 hours
15 hours

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 Equations", "Logarithmic Equations" ], "new_concepts": [], "current_concepts": [ "Exponential Growth", "Exponential Equations", "Logarithmic Equations" ] } ## Set up the equation with the given values $$ \begin{aligned} N(h) &= 450 \ 100e^{0.25h} &= 450 \end{aligned} $$ ## Isolate the exponential term $$ \begin{aligned} e^{0.25h} &= \frac{450}{100} \ e^{0.25h} &= 4.5 \end{aligned} $$ ## Solve for h using natural logarithms $$ \begin{aligned} 0.25h &= \ln(4.5) \ h &= \frac{\ln(4.5)}{0.25} \ h &\approx \frac{1.504077}{0.25} \ h &\approx 6.016 \approx 6 \end{aligned} $$

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

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QUESTION IMAGE

Question

Explanation:

Set up the equation with the given values

Isolate the exponential term

Solve for h using natural logarithms

Answer: