An algorithm on a social media site is set up so that the more shares a video receives, the more individuals the video is presented to on their feed. The views of a particular video are increasing at an exponential rate of 100% for each share the video receives. If the video originated with 10 views, the situation can be modeled by the exponential equation v(s)=10(2)s

Question

where v is the number of views for every s shares. Which of the following statements is true about the equation?

(1 point)
Responses

The domain (s-values) includes the values (s≥0)
.
The domain ( s -values) includes the values left parenthesis s greater-than-or-equal-to 0 right parenthesis .

The range (v-values) is all real numbers.
The range ( v -values) is all real numbers.

The domain (s-values) is all real numbers.
The domain ( s -values) is all real numbers.

The range (v-values) includes the values greater than (0<v≤10)
.

Answer 1

To analyze the given equation \( v(s) = 10(2^s) \), we can determine the domain and range of the function.

1. Domain:

   • The variable \( s \) represents the number of shares a video receives. Since it is not possible to have a negative number of shares, \( s \) must be greater than or equal to 0. Therefore, the domain of \( s \) is \( s \geq 0 \).

2. Range:

   • The function \( v(s) = 10(2^s) \) starts from 10 when \( s = 0 \) (because \( 2^0 = 1 \)). As the number of shares \( s \) increases, \( v(s) \) increases exponentially because \( 2^s \) grows very rapidly. Thus, the minimum value of \( v(s) \) is 10, and there is no upper limit as \( s \) can increase indefinitely. Therefore, the range of \( v(s) \) is \( v \geq 10 \).

Based on this analysis, the correct statement about the equation is:

The domain (s-values) includes the values (s ≥ 0).