To determine the number of people who had viewed the video once it had been online for 20 days, we'll use the provided function [tex]\( f(x) = 33 \times (1.3)^x \)[/tex].
Here are the steps:
1. Identify the given function: The function modeling the views is [tex]\( f(x) = 33 \times (1.3)^x \)[/tex], where [tex]\( x \)[/tex] is the number of days the video has been online.
2. Substitute the number of days: We need to find the number of views when [tex]\( x = 20 \)[/tex].
3. Perform the substitution: Replace [tex]\( x \)[/tex] with 20 in the function:
[tex]\[
f(20) = 33 \times (1.3)^{20}
\][/tex]
4. Calculate the exponent: Compute [tex]\( (1.3)^{20} \)[/tex].
5. Multiply by the initial value: Multiply the result from step 4 by the initial value, 33.
Following these steps, the calculated number of views is:
[tex]\[
f(20) = 33 \times (1.3)^{20} \approx 6271.638
\][/tex]
Therefore, the number of people who had viewed the video once it had been online for 20 days is approximately 6,271.
Thus, the correct answer is:
[tex]\[
\boxed{6271}
\][/tex]
