a decimal approximation for $\sqrt{15}$ is $3.8729833$. use a calculator to find $2^{3.9}$, $2^{3.87}$, $2^{3.873}$, $2^{3.87298}$, and $2^{3.8729833}$. now find $2^{\sqrt{15}}$. what do you observe?

$2^{3.9} = 14.928528$ (round to six decimal places as needed.)
$2^{3.87} = $ (round to six decimal places as needed.)

Question

a decimal approximation for $\sqrt{15}$ is $3.8729833$. use a calculator to find $2^{3.9}$, $2^{3.87}$, $2^{3.873}$, $2^{3.87298}$, and $2^{3.8729833}$. now find $2^{\sqrt{15}}$. what do you observe?

$2^{3.9} = 14.928528$ (round to six decimal places as needed.)
$2^{3.87} = $   (round to six decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Exponential Approximations", "Irrational Exponents" ], "current_concepts": [ "Exponential Approximations", "Irrational Exponents" ] } ## Calculate the value of the exponential expression $$ 2^{3.87} \approx 14.6211836... $$ ## Round to six decimal places $$ 2^{3.87} \approx 14.621184 $$ $2^{3.87} =$ $14.621184$ (Round to six decimal places as needed.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Approximations" ] }

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Question

Explanation:

Calculate the value of the exponential expression

Round to six decimal places

Answer: