### Home > INT3 > Chapter 7 > Lesson 7.2.3 > Problem7-84

7-84.

Barnaby’s grandfather is always complaining that $50$ years ago, he could buy his girlfriend dinner for only $1.50$. Now that same dinner costs $25.25$.

1. Assuming the price has increased exponentially and that same dinner never cost less than $0.20$, write the equation of a function that models the cost in relationship to the number of years from now.

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 $y = ab^{x} + k$.

Use the points $\left(−50, 1.50\right)$ and $\left(0, 25.25\right)$. The horizontal asymptote (or vertical shift in this case) is $y = 0.20$ (or $k = 0.20$).

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

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

Answers vary depending on precision used, about $874.64.$