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

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 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 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.

Answer 1

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

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

In exponential growth models, the growth rate accelerates over time, meaning that the number of wasps will increase rapidly as time goes on, particularly after the initial stages. Therefore, as \( t \) increases, the growth will start off relatively slow but will begin to increase more quickly, leading to a larger number of wasps over time.