the table represents an exponential function.

\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & \frac{3}{2} \\
\hline
2 & \frac{9}{8} \\
\hline
3 & \frac{27}{32} \\
\hline
4 & \frac{81}{128} \\
\hline
\end{array}

what is the multiplicative rate of change of the function?

$\bigcirc$ $\frac{2}{3}$
$\bigcirc$ $\frac{3}{4}$
$\bigcirc$ $\frac{4}{3}$
$\bigcirc$ $\frac{3}{2}$

Question

the table represents an exponential function.

\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & \frac{3}{2} \\
\hline
2 & \frac{9}{8} \\
\hline
3 & \frac{27}{32} \\
\hline
4 & \frac{81}{128} \\
\hline
\end{array}

what is the multiplicative rate of change of the function?

$\bigcirc$ $\frac{2}{3}$
$\bigcirc$ $\frac{3}{4}$
$\bigcirc$ $\frac{4}{3}$
$\bigcirc$ $\frac{3}{2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Multiplicative Rate of Change" ], "new_concepts": [], "current_concepts": [ "Exponential Functions", "Multiplicative Rate of Change" ] } ## Identify consecutive terms from the table $$ \begin{aligned} y_1 &= \frac{3}{2} \ y_2 &= \frac{9}{8} \end{aligned} $$ ## Calculate the ratio of consecutive terms $$ \begin{aligned} r &= \frac{y_2}{y_1} \ r &= \frac{\frac{9}{8}}{\frac{3}{2}} \ r &= \frac{9}{8} \times \frac{2}{3} \ r &= \frac{18}{24} = \frac{3}{4} \end{aligned} $$ ## Verify with subsequent terms $$ \begin{aligned} r &= \frac{y_3}{y_2} = \frac{\frac{27}{32}}{\frac{9}{8}} = \frac{27}{32} \times \frac{8}{9} = \frac{3}{4} \ r &= \frac{y_4}{y_3} = \frac{\frac{81}{128}}{\frac{27}{32}} = \frac{81}{128} \times \frac{32}{27} = \frac{3}{4} \end{aligned} $$

(A) $\frac{2}{3}$

(B) $\frac{3}{4}$

(C) $\frac{4}{3}$

(D) $\frac{3}{2}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Multiplicative Rate of Change" ] }

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QUESTION IMAGE

Question

Explanation:

Identify consecutive terms from the table

Calculate the ratio of consecutive terms

Verify with subsequent terms

Answer: