Use the table to answer the question.

Question

x h(x)=18x

2 324
2.7 2,450.393
2.71 2,522.252
2.718 2,581.254
2.7183 2,583.493
2.71828 2,583.343
2.718282 2,583.358
2.7182818 2,583.357
2.71828183 2,583.357
2.718281828 2,583.357
Consider the function h(x)=18x
. Given is a table with x-values that get closer to e≈2.71828182
(Euler’s number) and their corresponding h(x)
values. Use the sequence in the table to approximate 18e
correct to three decimal places.

(1 point)
Responses

2,583
2,583

2.718
2.718

2,583.357
2,583.357

324

Answer 1

To approximate \(18e\) using the provided table values for \(h(x) = 18x\) as \(x\) approaches \(e \approx 2.71828182\), we can focus on the last value in the list which corresponds closely to \(e\).

Looking at the values in the table:

• The \(h(x)\) value for \(x = 2.718281828\) is \(2,583.357\).

Since this value is the closest to when \(x\) approaches \(e\), we can use it as our approximation for \(18e\).

Therefore, the approximation of \(18e\) correct to three decimal places is:

2,583.357