which is the graph of $f(x) = 5(2)^x$?

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Exponential Functions", "y-intercept" ], "new_concepts": [], "current_concepts": [ "Exponential Functions", "y-intercept", "Exponential Growth" ] } ## Evaluate the function at x = 0 $$ f(0) = 5(2)^0 = 5(1) = 5 $$ ## Evaluate the function at x = 2 $$ f(2) = 5(2)^2 = 5(4) = 20 $$ ## Match points with the given graph $$ \begin{aligned} &\text{Point 1: } (0, 5)\ &\text{Point 2: } (2, 20) \end{aligned} $$

The shown graph is the correct graph of $f(x) = 5(2)^x$ because it passes through $(0, 5)$ and $(2, 20)$.

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "5*Math.pow(2, x)", "latex": "5\cdot 2^x" }, -5, 4 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "point", "params": [ [0, 5] ], "properties": { "name": "(0, 5)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [ [2, 20] ], "properties": { "name": "(2, 20)", "size": 4, "color": "#F2557F", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Functions" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Evaluate the function at x = 0

Evaluate the function at x = 2

Match points with the given graph

Answer: