To analyze the given equation \( W(t) = 5000 \times 1.13^t \), where \( W(t) \) represents the number of wasps at time \( t \) in months, we can make a few observations:
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Growth Rate: The growth rate of the wasp population is 13% per month. Since the base of the exponent is 1.13, this confirms that the population increases by 13% each month.
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Initial Value: At \( t = 0 \), the number of wasps is: \[ W(0) = 5000 \times 1.13^0 = 5000 \times 1 = 5000. \] So, the initial number of wasps is indeed 5000.
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Exponential Growth: The equation models exponential growth, which means that as time increases, the population will grow increasingly faster. This can be observed by taking the derivative or simply noting that the population growth is multiplicative rather than additive.
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Long-term Behavior: As \( t \) becomes large, \( W(t) \) will increase significantly due to the nature of exponential growth. This means that the population will soon grow to much larger numbers if the growth rate and conditions remain constant.
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Doubling Time: The doubling time can be estimated using the Rule of 70 (approximately). With a 13% growth rate, the doubling time will be around \( \frac{70}{13} \approx 5.38 \) months.
Now, based on these observations, without specific statement options provided, the following statements could be considered true regarding the equation:
- The population of wasps increases by 13% each month.
- When \( t = 0 \), the population is 5,000 wasps.
- The population will continue to grow exponentially over time.
- The population will double in approximately 5.38 months.
If you have specific statements in mind to evaluate, feel free to share them!