select the correct answer.

which exponential function has the greatest average rate of change over the interval $0, 2$?

$j(x) = 3(1.6)^x$

an exponential function, $f$, with a $y$-intercept of 1.5 and a common ratio of 2.

$\begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline g(x) & 8 & 10 & \frac{25}{2} & \frac{125}{8} \\ \hline \end{array}$

Question

select the correct answer.

which exponential function has the greatest average rate of change over the interval $0, 2$?

$j(x) = 3(1.6)^x$

an exponential function, $f$, with a $y$-intercept of 1.5 and a common ratio of 2.

$\begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline g(x) & 8 & 10 & \frac{25}{2} & \frac{125}{8} \\ \hline \end{array}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Average Rate of Change" ], "new_concepts": [], "current_concepts": [ "Average Rate of Change", "Exponential Functions" ] } ## Calculate average rate of change for $j(x)$ $$ \begin{aligned} j(0) &= 3(1.6)^0 = 3 \ j(2) &= 3(1.6)^2 = 3(2.56) = 7.68 \ \text{Rate}_{j} &= \frac{j(2) - j(0)}{2 - 0} = \frac{7.68 - 3}{2} = 2.34 \end{aligned} $$ ## Calculate average rate of change for $f(x)$ $$ \begin{aligned} f(x) &= 1.5(2)^x \ f(0) &= 1.5 \ f(2) &= 1.5(2)^2 = 6 \ \text{Rate}_{f} &= \frac{f(2) - f(0)}{2 - 0} = \frac{6 - 1.5}{2} = 2.25 \end{aligned} $$ ## Calculate average rate of change for $g(x)$ and $k(x)$ $$ \begin{aligned} g(0) &= 8 \ g(2) &= \frac{25}{2} = 12.5 \ \text{Rate}_{g} &= \frac{12.5 - 8}{2} = 2.25 \ k(0) &= 4 \ k(2) &= 9 \ \text{Rate}_{k} &= \frac{9 - 4}{2} = 2.5 \end{aligned} $$

(A) $j(x) = 3(1.6)^x$

(B) An exponential function, $f$, with a $y$-intercept of 1.5 and a common ratio of 2.

(C) The function $g(x)$ represented in the table.

(D) The function $k(x)$ represented in the graph.

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate average rate of change for \(j(x)\)

Calculate average rate of change for \(f(x)\)

Calculate average rate of change for \(g(x)\) and \(k(x)\)

Answer: