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Marta's mother shared a funny video of their cat on the Internet. The total number of people who had viewed the video over the first 30 days could be modeled using the function [tex]f(x) = 33(1.3)^x[/tex] where [tex]x[/tex] is the number of days the video has been online.

About how many people had viewed the video once it had been online for 20 days?

A. 190
B. 858
C. 6,271
D. 86,460

Sagot :

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]