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 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.
As t increases, w increases slowly at first and then quickly.
As t increases, w decreases quickly at first and then slowly.
1 answer
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.
Since the growth is exponential, the number of wasps will initially increase at a moderate rate, but as time goes on, the amount increases more rapidly because each month the population is growing by 13% of its previous month's count. Thus, the increase in the number of wasps accelerates over time.
