A small nest of wasps has an exponential growth rate of 13% per month. If the nest currently has 5000 wasps, the situation can be modeled by which equation?

Question

(1 point)
Responses

w(t) = 5000(13)t where w(t) is the number of wasps after t months
w(t) = 5000(13)t where w(t) is the number of wasps after t months

w(t) = 5000(1.13)t where w(t) is the number of wasps after t months
w(t) = 5000(1.13)t
where w(t) is the number of wasps after t months

w(t) = 5000(87)t where w(t) is the number of wasps after t months
w(t) = 5000(87)t where w(t) is the number of wasps after t months

w(t) = 50(1.13)t where w(t) is the number of wasps after t months

Answer 1

The correct equation to model the exponential growth of the wasp nest is:

w(t) = 5000(1.13)^t

where w(t) is the number of wasps after t months.

This equation reflects a starting population of 5000 wasps that grows by a factor of 1.13 each month, representing a 13% growth rate.

Answer 2

Which of the following statements is true about the above wasp 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
As t increases, w decreases quickly at first and then slowly
Question 3
25.

Answer 3

The true statement about the wasp equation \( w(t) = 5000(1.13)^t \) is:

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

This is characteristic of exponential growth, where the rate of increase becomes more rapid as time progresses. Initially, the growth might seem gradual, but as the population grows larger, the number of wasps increases more quickly.