To analyze the given equation \( w(t) = 5,000(1.13)^t \) for the growth of wasps, let's evaluate the statements provided:
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Domain of \( t \):
- The variable \( t \) represents time in months and cannot be negative due to the context (you can’t have negative time). Therefore, the valid values for \( t \) are \( t \geq 0 \).
- The correct statement here would be that the domain (t-values) includes the values of \( t \) such that \( t \geq 0 \).
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Range of \( w \):
- The function \( w(t) = 5,000(1.13)^t \) represents an exponential growth model, and as \( t \) increases, \( w(t) \) will continue to increase beyond 5,000. When \( t = 0 \), \( w(0) = 5,000 \cdot (1.13)^0 = 5,000 \).
- The smallest value of \( w(t) \) occurs at \( t = 0 \) and is \( 5,000 \). As \( t \) increases, \( w(t) \) will approach infinity, so \( w \) will be greater than 5,000 indefinitely.
- The range of \( w(t) \) is therefore \( w > 5,000 \), and it can never be less than or equal to 5,000.
Based on this analysis, the true statements among the given options are:
- The domain (t-values) includes the values of \( t \) such that \( t \geq 0 \).
- The range (w-values) does not include all real numbers and is not limited to values less than or equal to 5,000; thus, the other options regarding the range are false.
Therefore, the correct conclusion is:
- The domain (t-values) includes the values of t such that t ≥ 0.