Cynthia is working with a bacterial population. She was able to model the growth of her last batch using the function f(w)=100 (1.5)w, where w is the time in weeks and f(w) was the number of bacteria. She is about to start a new batch and would like to maximize how much bacteria she has after 10 weeks. She has a limited budget and can afford to either change her starting amount of bacteria to 500 or use a treatment that will change the growth rate to 1.8. Part A: Write new functions based on the original function, one where she changes her starting amount of bacteria to 500 and the other where she changes the growth rate to 1.8.

Part B: Which would produce more bacteria in 10 weeks?

For Part B, show your solving process (algebraic steps, diagrams, models, graphs, tables, and/or any other problem-solving tools you used) and state your answer to the question as a complete sentence.