Question

Irrational Exponents Quick Check
4 of 54 of 5 Items






Question
Use the table to answer the 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

2,583.357
2,583.357

2,583
2,583

324
324

2.718
2.718
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Answer 1

To approximate \( 18e \) using the values provided in the table, we can look at the \( h(x) = 18^x \) values corresponding to \( x \) values that get closer to \( e \approx 2.71828182 \).

From the table, we see:

- \( h(2.718) = 2,581.254 \)
- \( h(2.7183) = 2,583.493 \)
- \( h(2.71828) = 2,583.343 \)
- \( h(2.718282) = 2,583.358 \)
- \( h(2.7182818) = 2,583.357 \)
- \( h(2.71828183) = 2,583.357 \)
- \( h(2.718281828) = 2,583.357 \)

As \( x \) approaches \( e \), the values of \( h(x) \) seem to stabilize around \( 2,583.357 \).

Thus, the best approximation for \( 18e \) correct to three decimal places is:

**2,583.357**