The equation you've provided appears to describe the growth of a wasp nest based on a compound growth model, where \( W(t) \) is the number of wasps after \( t \) months, starting with an initial count of 5,000 wasps and growing at a rate of 13% per month.
The equation can be clearly stated as:
\[ W(t) = 5000 \times (1.13)^t \]
Here, \( 5000 \) is the initial number of wasps, \( 1.13 \) represents the growth factor (100% + 13% = 113% expressed as a decimal), and \( t \) is the time in months.
From this equation, we can derive several statements about the population of the wasp nest:
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Exponential Growth: The number of wasps in the nest grows exponentially over time due to the 13% growth rate. This means that as time increases, the increase in the number of wasps becomes more significant.
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Long-term Growth: As \( t \) increases, \( W(t) \) will increase rapidly. This means after several months, the population of wasps will be significantly larger than 5,000.
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Doubling Time: You can calculate roughly how long it would take for the wasp population to double by finding the time \( t \) when \( W(t) = 10000 \). This involves solving the equation \( 5000 \times (1.13)^t = 10000 \).
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Initial Population: At \( t = 0 \), \( W(0) = 5000 \). This indicates that the nest starts with 5,000 wasps, which confirms that the initial condition is modeled correctly.
If you are looking for a specific true statement among several options, please provide the options, and I can help identify which statement is accurate concerning the growth model.