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 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 decreases quickly at first and then slowly.

Answer 1

To analyze the equation \( w(t) = 5,000(1.13)^t \), we need to consider the nature of exponential growth.

Since the growth rate is 13% per month, the value of \( w(t) \) is increasing as \( t \) increases. In the context of exponential growth, the function initially grows at a slower pace because it starts from a lower number. However, as time goes on, the number of wasps (or whatever is being modeled) grows more rapidly due to the compounding effect of the growth rate.

Therefore, the correct statement is:

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