To approximate \( 2^{19} \), we need to find a sequence of \( x \)-values that approaches a point such that \( f(x) = 2^x \) is close to \( 2^{19} \).
Let's analyze the given options:
-
4, 4.4, 4.36, 4.359, 4.3589, 4.35890
- These values are in the range of 4, which won't yield an approximation for \( 2^{19} \).
-
3, 3.9, 3.87, 3.873, 3.8730, 3.87298
- These values are also in the range of around 3, which again won't be close to \( 2^{19} \).
-
4, 4.1, 4.12, 4.123, 4.1231, 4.12311
- While these are increasing, they still do not approach 19.
-
16, 21.1, 20.53, 20.521, 20.5191, 20.51916
- This is the only sequence that includes numbers close to 20, which would approximate \( 2^{19} \) (since \( 2^{19} = 524288 \) and \( 2^{20} = 1048576 \)).
Thus, the best choice for approximating \( 2^{19} \) is:
16, 21.1, 20.53, 20.521, 20.5191, 20.51916