The general form of an exponential equation is y=ab^x.
Equation: y=128( 12)^x
There are 16 teams left after the third round.
Practice makes perfect
Writing the Equation
Our starting value is 128, and then after each round half of the teams are eliminated. Let's form an equation where y represents the amount left and x represents each round. We will use the general form of an exponential equation.
y=ab^x
After the 0^(th) round, there should still be 128 teams left. This tells us that when x=0, y=128.
128=ab^0 ⇒ 128=a
Let's substitute this for the a-value in our equation.
y=128b^x
Recall that after each round the amount of teams remaining is cut in half. This tells us that when x=1, y should be 1282. Similarly, when x=2, y should be 1282* 12. We can see that each time x increases we will multiply by 12.
y=128 * 1/2 * 1/2 * 1/2 * . . . * 1/2 x times
⇓
y=128(1/2)^x
