To approximate \( 2^{19} \) (which is the same as \( 219\sqrt{} \)), we want to find a sequence of \( x \)-values that leads to \( f(x) = 2^x \) being close to \( 2^{19} \).
Since \( 2^{19} \) is a large number, we expect \( x \) to be close to 19.
Here are the options:
- 4, 4.1, 4.12, 4.123, 4.1231, 4.12311
- 3, 3.9, 3.87, 3.873, 3.8730, 3.87298
- 16, 21.1, 20.53, 20.521, 20.5191, 20.51916
- 4, 4.4, 4.36, 4.359, 4.3589, 4.35890
Among these options, only option 3 includes values that are around 19 (specifically 16 and values close to 21). Therefore, the correct choice for a sequence of \( x \)-values that can be used to approximate \( 2^{19} \) is:
16, 21.1, 20.53, 20.521, 20.5191, 20.51916
1 answer