Final answer:
The boys will get to play video games for approximately 7 days before they are allowed less than 15 minutes of game time.
Step-by-step explanation:
To find out how many days the boys will get to play video games before they are allowed less than 15 minutes of game time, we will set up an equation. The boys start with 2.5 hours of game time on Monday. Then, their time is cut in half each day. So, the total game time on Tuesday is 2.5/2 hours, on Wednesday is (2.5/2)/2 hours, and so on. We need to find when the game time drops below 15 minutes, which is 0.25 hours. Let's set up the equation:
2.5 * (1/2)^x = 0.25
where x is the number of days.
By simplifying the equation, we get:
(1/2)^x = 0.1
To solve for x, we need to take the logarithm of both sides:
log((1/2)^x) = log(0.1)
x * log(1/2) = log(0.1)
x = log(0.1) / log(1/2)
By calculating this expression, we get x ≈ 6.64. Since we can't have a fractional number of days, we round up to the nearest whole number. Therefore, the boys will get to play video games for approximately 7 days before they are allowed less than 15 minutes of game time.