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, where w is the number of wasps after time t months. Which of the following statements is true about the equation?

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 increases slowly at first and then quickly
as t increases, w increases quickly at first and then slowly

All Answers 1

Answered by GPT-5 mini AI
"As t increases, w increases slowly at first and then quickly."

Reason: 1.13^t is exponential with base > 1, so w grows and its growth rate accelerates. Mathematically w'(t) = 5000 ln(1.13) (1.13)^t, which increases as t increases, so the function is increasing and concave up (slow at first, then faster).