question 20

the equation $y = 4 \cdot 3^t$ shows the number of infected people from an outbreak of the measles. the variable $y$ represents the number of infected people, and $t$ represents time in weeks.

in how many weeks will the number of infected people reach 600?

- 3.52 weeks
- 4.02 weeks
- 4.56 weeks
- 3.91 weeks

Question

question 20

the equation $y = 4 \cdot 3^t$ shows the number of infected people from an outbreak of the measles. the variable $y$ represents the number of infected people, and $t$ represents time in weeks.

in how many weeks will the number of infected people reach 600?

- 3.52 weeks
- 4.02 weeks
- 4.56 weeks
- 3.91 weeks

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponential Equations", "Logarithmic Equations", "Logarithm Properties" ], "new_concepts": [], "current_concepts": [ "Exponential Equations", "Logarithmic Equations", "Logarithm Properties" ] } ## Set up the equation Using the **Exponential Equations** knowledge point $$ \begin{aligned} y &= 4 \cdot 3^t \ 600 &= 4 \cdot 3^t \end{aligned} $$ ## Isolate the exponential term Using the **Exponential Equations** knowledge point $$ \begin{aligned} \frac{600}{4} &= 3^t \ 150 &= 3^t \end{aligned} $$ ## Apply logarithms to solve for t Using the **Logarithmic Equations** and **Logarithm Properties** knowledge points $$ \begin{aligned} \ln(150) &= \ln(3^t) \ \ln(150) &= t \ln(3) \ t &= \frac{\ln(150)}{\ln(3)} \end{aligned} $$ ## Calculate the numerical value Using the **Logarithmic Equations** knowledge point $$ \begin{aligned} t &\approx \frac{5.010635}{1.098612} \ t &\approx 4.56087 \approx 4.56 \text{ weeks} \end{aligned} $$

3.52 weeks

4.02 weeks

4.56 weeks

3.91 weeks

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

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QUESTION IMAGE

Question

Explanation:

Set up the equation

Isolate the exponential term

Apply logarithms to solve for t

Calculate the numerical value

Answer: