Brianna is babysitting for her calculus teacher because she broke her phone and needs to buy a new one. She will get paid at a flat rate of $\$3.50$ per hour, per child. Natalie is away at a friend’s house for the first two hours while Brianna is babysitting Morgan and Lydia. Natalie returns and Brianna continues to babysit for three additional hours.

1. Sketch a graph and write a piecewise function to represent Brianna’s pay rate.

2. How much will Brianna get paid for the five hours of work?

3. Represent Brianna’s total pay using definite integrals.