The equation p equals 25 times 3 to the power of n shows the number of points available in round n of the game show, where each round has 3 times as many points as the previous round.
To express the relationship between the round number (n) and the points available (p) in the game show, we can use an exponential function since the points available in each round are a multiple of the previous round.
Let's analyze the pattern in the points available:
In Round 0 (n=0), there are 25 points.
In Round 1 (n=1), there are 3 times as many points as in Round 0, i.e., 25 times 3 equals 75.
In Round 2 (n=2), there are 3 times as many points as in Round 1, i.e., 75 times 3 equals 225.
In Round 3 (n=3), there are 3 times as many points as in Round 2, i.e., 225 times 3 equals 675.
This pattern indicates that the points available in each round form a geometric sequence, where each term is 3 times the previous term. The general form of a geometric sequence is given by:
p equals a times r to the power of n.
Where:
p is the points available in round n,
a is the initial term of the sequence (25 points in Round 0),
r is the common ratio (3, as each round has 3 times as many points), and
n is the round number.
Thus, the equation that represents the number of points available p in round n of the game show is:
p equals 25 times 3 to the power of n.
The question probable may be:
In a game show, players play multiple rounds to score points. Each round has 3 times as many points available as the previous round.
Round 0 1 2 3 n
Points 25 75 225 675
Which equation shows the number of points available, p, in round n of the game show?