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
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.
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.
Answers
GPT-4o mini
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.
**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.