A small nest of wasps has an exponential growth rate of 13% per month. If the nest currently has 5,000 wasps, the situation can be modeled by the equation w(t)=5,000(1.13)^t

Question

A small nest of wasps has an exponential growth rate of 13% per month. If the nest currently has 5,000 wasps, the situation can be modeled by the equation  w(t)=5,000(1.13)^t
 , where w is the number of wasps after t months. Which of the following statements is true about the equation?(1 point)

GPT-4o mini · Answer

To analyze the equation $ w(t) = 5000(1.13)^t $, we can assess several aspects of the model. 1. **Growth Rate**: The growth rate is described as 13% per month. This means that every month, the population of wasps increases by 13%. The factor $ 1.13 $ indicates that the number of wasps increases to 113% of its previous amount each month. 2. **Initial Population**: At $ t = 0 $, the number of wasps is $ w(0) = 5000(1.13)^0 = 5000(1) = 5000 $. This confirms that the initial population is indeed 5,000. 3. **Nature of Growth**: The equation represents exponential growth, not linear growth. This means that the population will increase more rapidly over time as compared to a linear growth model. 4. **Mathematical Interpretation**: The expression $ 1.13 $ is the base of the exponential growth factor, indicating that it is a multiplicative growth over time. Given the nature of the equation and these breakdowns, the most accurate statement that can be derived about the equation is that it models **exponential growth** of the wasp population, specifically that the population increases by 13% each month. If there are specific options to choose from, please provide them, and I can help you identify which one is correct based on the analysis above!