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

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

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

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

Answer 1

The correct statement regarding the behavior of the equation \( w(t) = 5,000(1.13)^t \) is:

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

This is because the growth is exponential, meaning that as time progresses, the number of wasps increases rapidly at first due to the compounding effect of the growth rate, and as the population becomes larger, the rate of increase becomes relatively slower compared to earlier stages.