Question

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?

Answer 1

Answer:

$p = 25(3)^n$

Step-by-step explanation:

Given

Round 0 1 2 3

Points 25 75 225 675

Required

Determine the equation

Let n = rounds and p = points.

So, we have:

$(n_1,p_1) = (0,25)$

$(n_2,p_2) = (1,75)$

$(n_2,p_2) = (3,225)$

The above shows a geometric progression.

So, we solve using

$p = ab^n$

In $(n_1,p_1) = (0,25)$

n = 0 and p = 25

Substitute these values in $p = ab^n$

$25 = ab^0$

$25 = a*1$

$25 = a$

$a = 25$

In $(n_2,p_2) = (1,75)$

n = 1 and p = 75

Substitute these values in $p = ab^n$

$75 = ab^1$

$75 = ab$

Substitute 25 for a

$75 = 25*b$

Make b the subject

$b = \frac{75}{25}$

$b = 3$

So, we have:

$a = 25$ and $b = 3$

The equation $p = ab^n$ becomes

$p = 25(3)^n$