To evaluate the statements based on the population model \( p(t) = 60(0.92)^t \), let’s analyze each statement:
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Statement #1: As t increases, p increases slowly at first, then quickly.
- False: The population is decreasing, not increasing.
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Statement #2: The y-intercept is greater than 0.
- True: When \( t = 0 \), \( p(0) = 60(0.92)^0 = 60 \). The y-intercept (population at year 0) is 60, which is greater than 0.
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Statement #3: There is a horizontal asymptote at p = 0.
- True: As \( t \) approaches infinity \( (t \to \infty) \), \( p(t) \) approaches 0, indicating a horizontal asymptote at \( p = 0 \).
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Statement #4: As t increases, p decreases at a decreasing rate.
- True: The population decreases by a constant percentage (8% per year), which means it decreases at a decreasing rate rather than a constant amount.
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Statement #5: The p-values include all real numbers.
- False: The population \( p(t) \) can never be negative or exceed 60, so the p-values are restricted to the interval \( (0, 60] \).
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Statement #6: The graph decreases without bound as t approaches positive infinity.
- True: While the population approaches 0, it does decrease continuously but does not go below 0. It "approaches" 0 without actually reaching it.
Now, let's summarize the true statements:
- True Statements: 2, 3, 4, and 6
- False Statements: 1 and 5
Given this analysis, the correct answer is:
A: The true statements are 2, 3, 4, and 6.