A new video game was released. The number of games remaining at a local store $x$ hours after opening is given by the function $f(x) = 250(0.8)^x$. We need to evaluate the given statements A, B, and C based on this function.

1. Problem Description

A new video game was released. The number of games remaining at a local store $x$ hours after opening is given by the function $f(x) = 250(0.8)^x$. We need to evaluate the given statements A, B, and C based on this function.

2. Solution Steps

A. The store initially had 250 games.

Initially means at the opening, so $x=0$.

$f(0) = 250(0.8)^0 = 250(1) = 250$.

The statement is true.

B. The number of games decreases by 80% each hour.

The function is $f(x) = 250(0.8)^x$.

Since $0.8 = 1 - 0.2$, the number of games remaining is 80% of the number of games in the previous hour. Therefore, the number of games decreases by 20% each hour, not 80%. The statement is false.

C. After 2 hours, the store had 160 games remaining.

We need to calculate $f(2)$.

$f(2) = 250(0.8)^2 = 250(0.64) = 160$.

The statement is true.

3. Final Answer

A. The store initially had 250 games: True

B. The number of games decreases by 80% each hour: False

C. After 2 hours, the store had 160 games remaining: True