Determine which type of function—linear, quadratic, or exponential—would be best for modeling each situation below. You do not need to write an equation for the situation.

1. Bailey is growing bacteria on a petri dish for science class. The population of bacteria doubles every $20$ minutes, so the initial number of bacteria is $1000$, then $2000$, then $4000$, then $8000$, etc.

   Hint (a):

   What does the pattern $1000$, $2000$, $4000$ imply?

2. Avery is working on her math homework. She finished nine problems in class. She knows that, on average, she can do three problems in five minutes.

   Hint (b):

   $3$ problems each $5$ minutes relates to slope.

3. Keiton loves catapults. He is building a small catapult that will launch an apple into the air and over the fence into his friend’s backyard.

   Hint (c):

   What kind of function represents the motion of an object under gravity?