Rip-Off Rentals charges $$25$ per day plus $50¢$ per mile to rent a mid-sized car. Your teacher will rent you his or her family sedan and charge you only $3¢$ if you drive one mile, $6¢$ if you drive two miles, $12¢$ if you drive three miles, $24¢$ for four miles, and so on.

1. Write equations that will allow you to calculate the cost of renting each car.

   Hint (a):

   Let $d =$ number of days, $m =$ number of miles, and $y =$ total cost.

   More Help (a):

   Your teacher is using a geometric sequence.

   Answer (a):

   $y = 25d + 0.5m$ and $y=0.03(2)^{m−1}$

2. If you plan to rent the car for a two-day road trip, which is the better deal if you drive $10$ miles? $20$ miles? $100$ miles?

   Hint (b):

   Substitute the values into each equation to see which rental costs less for each distance.