Question
A small mass of a wasp has an exponential growth rate of 13% per month if the nest currently has 5,000 w wasps the situation can be modeled by the equation WP = 5,000 * 1.13t where w is the number of walls after tea time months which of the following statements is true about the equation
Answers
GPT-4o mini
The equation you provided, \( W(t) = 5,000 \times 1.13^t \), is an exponential growth model where:
- \( W(t) \) represents the number of wasps after \( t \) months.
- The initial population of wasps is 5,000.
- The base of the exponent, \( 1.13 \), indicates that the population increases by 13% each month.
Here are some true statements about this equation:
1. **Initial Population**: At \( t = 0 \) (the starting point), the number of wasps is \( W(0) = 5,000 \). This indicates that the initial population of wasps in the nest is correctly represented in the equation.
2. **Growth Rate**: The population of wasps grows at an exponential rate of 13% per month. This means that each month, the population is multiplied by \( 1.13 \).
3. **Asymptotic Behavior**: As \( t \) increases, the population size \( W(t) \) will grow indefinitely, assuming there are no limiting factors (like resource availability or disease).
4. **Doubling Time**: The model allows for the calculation of doubling time using the rule of 70. You can find an approximate doubling time by dividing 70 by the growth rate percentage (in %), which would be around \( \frac{70}{13} \approx 5.38 \) months for this population to double.
5. **Continuous Growth**: The function assumes that the population is continuously growing without interruption, reflecting ideal conditions.
If you need more specific interpretations or analysis about this equation, please let me know!
- \( W(t) \) represents the number of wasps after \( t \) months.
- The initial population of wasps is 5,000.
- The base of the exponent, \( 1.13 \), indicates that the population increases by 13% each month.
Here are some true statements about this equation:
1. **Initial Population**: At \( t = 0 \) (the starting point), the number of wasps is \( W(0) = 5,000 \). This indicates that the initial population of wasps in the nest is correctly represented in the equation.
2. **Growth Rate**: The population of wasps grows at an exponential rate of 13% per month. This means that each month, the population is multiplied by \( 1.13 \).
3. **Asymptotic Behavior**: As \( t \) increases, the population size \( W(t) \) will grow indefinitely, assuming there are no limiting factors (like resource availability or disease).
4. **Doubling Time**: The model allows for the calculation of doubling time using the rule of 70. You can find an approximate doubling time by dividing 70 by the growth rate percentage (in %), which would be around \( \frac{70}{13} \approx 5.38 \) months for this population to double.
5. **Continuous Growth**: The function assumes that the population is continuously growing without interruption, reflecting ideal conditions.
If you need more specific interpretations or analysis about this equation, please let me know!