ALGEBRA2Scott and Greg are looking for summer jobs. Their father, who is head of the neighborhood beautification committee, says that if they pick up litter from around the neighborhood for a whole day, he will pay them $0.15 for each piece of trash they collect. Scott realizes that the more litter they pick up, the more difficult it will be to find more pieces, so he proposes a different payment scheme. "How about you give us$0.10 for the first piece, and increase our pay by 2% for each piece after that? Then we'll get paid more for the pieces we work harder to find." a. Write an equation to generate the series Scott is proposing. b. With Scott's plan, how much will his dad have to pay him for the 100th piece of litter he finds? For the 200th? c. If Scott collects 150 pieces of litter, how much will he have earned in total? What if he picks up 200 pieces? d. Greg thinks Scott is crazy to propose an increase of just 2% per piece. After all 2% of 10 cents is just $\frac { 2 } { 10 }$ of a cent! Instead, he plans to ask for a one-cent increase for every piece. If their father agrees to this, how much would Greg get paid for the 100th piece he collects? For the 200th piece? e. If the boys each collect 150 pieces of litter, which payment scheme will earn them the most money? f. What if they each pick up a total of 200 pieces?