Question

Enter an equation for the function. Give your answer in the form a(b)n. In the event that a = 1, give your answer in the form (b)n. The NCAA basketball tournament begins with 64 teams, and after each round, half the teams are eliminated. The number of remaining teams t(n) is an exponential function of the number n of rounds already played.

Answer 1

Answer: The equation is t(n) = 64(0.5)^n.

This is an example of an exponential equation because we are repeatedly multiplying the value by 1/2.  

Exponential equation take the form of y = ab^x, where a is the starting amount and b is the rate. 

In our case, we are starting with 64 and reducing half (0.5) of the teams each week.

This makes our equation: y = 64(0.5)^x