### Home > CAAC > Chapter 13 > Lesson 13.IF2-S > Problem6-31

6-31.

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.

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 $y=ab^x$.

Use the points $(−50,1.50)$ 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?

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

$\approx\425.04$