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

Answer 1

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!