Barnaby’s grandfather is always complaining that back when he was a teenager, he used to be able to buy his girlfriend dinner for only $\$1.50$.

1. If that same dinner that Barnaby’s grandfather purchased for $\$1.50$ sixty years ago now costs $\$25.25$, and the price has increased exponentially, write an equation that will give you the costs at different times.

   Hint (a):

   Begin by defining variables.
   Let $x=$ the number of years
   Let $y=$ the cost of a dinner
   You need to write an equation of the form $y=ab^x$.

   More Help (a):

   Use the points $(−60,1.50)$ and $(0,25.25)$ to write and solve a system of equations.

2. How much would you expect the same dinner to cost in $60$ years?

   Hint (b):

   Let $x=60$ in your equation from part (a).

   Answer (b):

   $\approx\$425.04$