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 time t months. Which of the following statements is true about the equation?(1 point) Responses As t increases, w increases quickly at first and then slowly. As t increases, w increases quickly at first and then slowly. As t increases, w increases slowly at first and then quickly. As t increases, w increases slowly at first and then quickly. As t increases, w decreases quickly at first and then slowly. As t increases, w decreases quickly at first and then slowly. As t increases, w decreases slowly at first and then quickly.

Answer 1

The equation given for the wasp population is \( w(t) = 5,000(1.13)^t \). This describes an exponential growth model, where the population of wasps increases by a factor of 1.13 each month.

In exponential growth scenarios, as time \( t \) increases, the growth rate also increases. Initially, when \( t \) is small, the population increases at a slower rate. However, as \( t \) becomes larger, the population grows more quickly due to the exponential factor.

Thus, the correct statement is:

As t increases, w increases slowly at first and then quickly.