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

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

Answer 1

The given equation is \( w(t) = 5,000(1.13)^t \).

This represents exponential growth since the base of the exponent (1.13) is greater than 1. As \( t \) increases, the term \( (1.13)^t \) grows larger, which means the number of wasps \( w \) increases over time.

Typically, in an exponential growth scenario, the quantity starts increasing slowly (for small values of \( t \)) but then starts increasing more rapidly as time goes on because the model is multiplicative.

Therefore, the correct statement is:

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