The equation \( w(t) = 5,000(1.13)^t \) represents exponential growth, where the population of wasps increases over time. As \( t \) increases, the value of \( (1.13)^t \) grows exponentially, meaning that the number of wasps \( w \) will increase rapidly as time progresses.
In exponential growth, the rate of increase becomes faster as time goes on—initially, the increase may seem slow, but it accelerates over time.
Therefore, the correct statement is:
As t increases, w increases quickly at first and then slowly.
This can be misleading because, in the context of the overall growth (exponential), it might seem like it increases slowly at first, but actually, it is always increasing and accelerates as \( t \) increases. The better interpretation is to say that as \( t \) increases, \( w \) increases very quickly and continuously.
If rewritten for clarity:
As t increases, w consistently increases rapidly without slowing down, contrary to any suggestion of slowing down later.
However, from the provided options, none perfectly capture the behavior of exponential growth. In the traditional sense of exponential growth, you would see the growth rate increase more and more rather than slow down.