Suppose the size of a pod of orca whales doubles every 90 months. Write an exponential function that models population of the pod if it starts with 20 orca whales. Write your equation using the doubling-time form \( f(x)=a(2)^{x / c} \). \[ f(x)= \]

To model the population of the pod of orca whales, we start with the initial population of 20. Given that the pod doubles every 90 months, we can use the provided doubling-time form of the equation. In this case, \( a = 20 \) (the initial number of orca whales) and \( c = 90 \) (the doubling time). Thus, the equation will be: \[ f(x) = 20(2)^{x / 90} \] Now, you can use this function to estimate how many orcas will be in the pod at any given time \( x \) in months! As a fun fact, orca whales are known for their complex social structures, much like human families. They often travel in pods that can include not just parents and their young, but also extended family members. This strong family bond is a key factor in their survival and can significantly influence the growth of their populations! For real-world application, this exponential growth model isn't just for orcas! It's used broadly in ecology to understand how animal populations can explode under certain conditions. But don’t forget: various factors like food availability, disease, and human impact can affect these models in practice. So while the math gives us a neat curve, nature loves to keep us guessing!