Question

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Answer 1

Answer:

Option A; the tournament did begin with 128 teams

Step-by-step explanation:

We can see that this equation is represented by compound interest, in other words an exponential function, either being exponential growth or exponential decay;

f ( x ) = a + ( b )^x, where a ⇒ start value, b ⇒ constant, x ⇒ ( almost always considered ) time, but in this case rounds

Option A; The equation is given to be t ( x ) = 128 * ( 1/2 )^x. Given by the above, 128 should represent the start value, hinting that the tournament did indeed begin with 128 teams

Option B; As the rounds increase the number of teams approach 128. Now mind you 128 is the start value, not the end value, which would mean that this statement is false

Option C; The tournament began with 1/2 teams. Theoretically that would not be possible, but besides that the tournament began with 128 teams, only differed by 1/2 times as much every round. This statement is thus false

Option D; This situation actually represents exponential decay. If each round the number of teams differed by 1/2 times as much, the number of teams remaining is less than before, and thus this models exponential decay, not growth ( statement is false )

Answer : Option A; the tournament did begin with 128 teams