A cell phone company charges $0.10 per text message if the customer sends up to 100 messages per month. The company charges $0.08 per text if a customer sends between 101 and 200 messages, and $0.06 per text if the customer sends between 201 and 300 messages. Today is the last day of the billing cycle.

a) Create a piecewise function to represent this situation.

b) If Tara has already sent 200 messages, is it worth it for her to send 1 more text message? Explain why or why