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, $24^{¢}$ for four, and so on.

1. Write a rule that will give you the cost to rent 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):

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

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.