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

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.

Answer 1

The given equation \( w(t) = 5,000(1.13)^t \) models the growth of the wasp population, where the growth factor is \( 1.13 \) (indicating a 13% increase per month).

In this model, as \( t \) increases, the value of \( (1.13)^t \) increases exponentially. This means that initially, the population will increase at a certain rate, but as time progresses, the absolute number of wasps grows larger, which causes the growth rate to appear to increase quickly.

Therefore, the correct interpretation is:

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

This statement captures the nature of exponential growth where, although the percentage increase remains constant, the actual increase grows larger over time. So, the correct response from the provided statements is:

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