the table shows the estimated number of lines of code written by computer programmers per hour when (x) people are working.

productivity
\begin{tabular}{|c|c|}
\hline
people working & lines of code written hourly \\
\hline
2 & 50 \\
\hline
4 & 110 \\
\hline
6 & 160 \\
\hline
8 & 210 \\
\hline
10 & 270 \\
\hline
12 & 320 \\
\hline
\end{tabular}

which model best represents the data?

$y = 47(1.191)^x$
$y = 34(1.204)^x$
$y = 26.9x - 1.3$
$y = 27x - 4$

Question

the table shows the estimated number of lines of code written by computer programmers per hour when (x) people are working.

productivity
\begin{tabular}{|c|c|}
\hline
people working & lines of code written hourly \\
\hline
2 & 50 \\
\hline
4 & 110 \\
\hline
6 & 160 \\
\hline
8 & 210 \\
\hline
10 & 270 \\
\hline
12 & 320 \\
\hline
\end{tabular}

which model best represents the data?

$y = 47(1.191)^x$
$y = 34(1.204)^x$
$y = 26.9x - 1.3$
$y = 27x - 4$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Rate of Change", "Linear Modeling", "Model Selection" ], "new_concepts": [], "current_concepts": [ "Linear Rate of Change", "Linear Modeling", "Model Selection" ] } ## Analyze the rate of change $$ \begin{aligned} &\Delta x = 4 - 2 = 2, \quad \Delta y = 110 - 50 = 60 \implies \frac{\Delta y}{\Delta x} = 30\ &\Delta x = 6 - 4 = 2, \quad \Delta y = 160 - 110 = 50 \implies \frac{\Delta y}{\Delta x} = 25\ &\Delta x = 8 - 6 = 2, \quad \Delta y = 210 - 160 = 50 \implies \frac{\Delta y}{\Delta x} = 25\ &\Delta x = 10 - 8 = 2, \quad \Delta y = 270 - 210 = 60 \implies \frac{\Delta y}{\Delta x} = 30\ &\Delta x = 12 - 10 = 2, \quad \Delta y = 320 - 270 = 50 \implies \frac{\Delta y}{\Delta x} = 25 \end{aligned} $$ ## Determine the model type and slope $$ \begin{aligned} &m_{\text{avg}} \approx \frac{30 + 25 + 25 + 30 + 25}{5} = 27\ &\text{Since the rate of change is approximately constant, a linear model is best.}\ &y = mx + b \implies y \approx 27x + b \end{aligned} $$ ## Evaluate the y-intercept $$ \begin{aligned} &50 = 27(2) + b \implies b = 50 - 54 = -4\ &y = 27x - 4 \end{aligned} $$

y = 47(1.191)^x

y = 34(1.204)^x

y = 26.9x - 1.3

y = 27x - 4

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Modeling" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the rate of change

Determine the model type and slope

Evaluate the y-intercept

Answer: