y = \frac{1}{8}e^x

y = \frac{1}{2}e^x

y = 2e^x

y = 8e^x

Question

y = \frac{1}{8}e^x

y = \frac{1}{2}e^x

y = 2e^x

y = 8e^x

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 Function Graphing" ], "new_concepts": [ "Exponential Curve Fitting" ], "current_concepts": [ "Exponential Function Graphing", "Exponential Curve Fitting" ] } ## Identify key points on the graph Using the **Exponential Function Graphing** knowledge point $$ \begin{aligned} &\text{At } x = 0, \quad y = 0.5 = \frac{1}{2}\ &\text{At } x = 1, \quad y \approx 1.36\ &\text{At } x = 2, \quad y \approx 3.69 \end{aligned} $$ ## Test the general equation form Using the **Exponential Function Graphing** knowledge point $$ \begin{aligned} &y = a e^x\ &\text{Substitute } (0, \frac{1}{2}):\ &\frac{1}{2} = a e^0 \implies a = \frac{1}{2} \end{aligned} $$ ## Verify with another point Using the **Exponential Function Graphing** knowledge point $$ \begin{aligned} &\text{For } y = \frac{1}{2}e^x:\ &\text{At } x = 2, \quad y = \frac{1}{2}e^2 \approx \frac{1}{2}(7.389) \approx 3.69 \end{aligned} $$ This matches the graph perfectly.

(A) $y = \frac{1}{8}e^x$

(B) $y = \frac{1}{2}e^x$

(C) $y = 2e^x$

(D) $y = 8e^x$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify key points on the graph

Test the general equation form

Verify with another point

Answer: