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

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

This is characteristic of exponential growth: initially, the quantity increases relatively fast, but as time goes on, the rate of increase becomes slower compared to previous periods, even though the overall quantity continues to grow.