Cynthia is working with a bacterial population. She was able to model the growth of her last batch using the function LaTeX: f\left(w\right)=100\left(1.5\right) ^wf ( w ) = 100 ( 1.5 ) w, where w is the time in weeks and f(w) was the amount 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, one for each of her two options.

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.