Bot GPT 4-o mini To analyze the given equation \( v(s) = 10(2^s) \) where \( v \) is the number of views and \( s \) is the number of shares, let's explore the domain and range:
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Domain:
- Since \( s \) represents the number of shares, it cannot be negative. The smallest value for shares is 0. Therefore, the domain of \( s \) is \( s \geq 0 \).
- This validates the first option: "The domain (s-values) includes the values \( s \geq 0 \)."
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Range:
- The function starts with 10 views when \( s = 0 \) (since \( v(0) = 10 \times 2^0 = 10 \)).
- As \( s \) increases, \( v(s) \) increases exponentially. Since \( 2^s \) will always be greater than or equal to \( 1 \) for \( s \geq 0 \), the minimum value of \( v(s) \) is 10.
- Thus, the range of views \( v \) starts from 10 and goes to infinity. This means the range is \( v \geq 10 \).
From this analysis, we can confirm that the other statements about the range are not correct, specifically:
- "The range (v-values) is all real numbers" is false because the minimum view is 10.
- "The range (v-values) includes the values greater than (0<v≤10)" is also false since the values start from 10.
- "The domain (s-values) is all real numbers" is false as negative shares do not make sense in this context.
Thus, the only true statement is: The domain (s-values) includes the values \( s \geq 0 \).
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