An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Analyze the given piecewise function and the provided statements.
Evaluate each statement against the function's definition.
Determine that the statement 'Any amount of time over an hour and a half would cost 1 0 ′ a cc u r a t e l yre f l ec t s t h e f u n c t i o n ′ s b e ha v i or f or t > 90$.
Conclude that the correct statement is: Any amount of time over an hour and a half would cost $10 .
Explanation
Understanding the Problem We are given a piecewise function that describes the cost, f ( t ) , to connect to the Internet at an online gaming store based on the time, t , in minutes. Our goal is to determine which of the provided statements accurately describes the cost function.
Analyzing Each Statement Let's analyze each statement:
It costs $5 per hour to connect to the Internet at the gaming store. This statement implies that $f(60) = 5 . According to the function definition, since 30 < 60 ≤ 90 , $f(60) = 5 . So, this statement is potentially true.
The first half hour is free, and then it costs $5 per minute to connect to the Internet. This statement implies that for 30"> t > 30 , the cost is $5 per minute. Let's test this for t = 31 . The cost should be $f(31) = 5 . According to the statement, the cost would be $(31-30)
less times $5 = 5 . Now let's test for t = 60 . The cost should be $f(60) = 5 . According to the statement, the cost would be $(60-30)
less times $5 = 150 . This contradicts the given function, so this statement is false.
It costs $10 for each 90 minutes spent connected to the Internet at the gaming store. This statement implies that $f(90) = 10 . According to the function definition, since 30 < 90 ≤ 90 , $f(90) = 5 . So, this statement is false.
Any amount of time over an hour and a half would cost $10. An hour and a half is 90 minutes. This statement implies that for 90"> t > 90 , $f(t) = 10 . According to the function definition, this is true.
Choosing the Most Accurate Statement Now we have two potentially true statements: 1 and 4. We need to choose the most accurate one.
Statement 1 says it costs $5 per hour. This is true for any time between 30 and 90 minutes. Statement 4 says any amount of time over an hour and a half would cost $10. This is true for any time greater than 90 minutes.
Since statement 4 accurately describes the cost for 90"> t > 90 , it is the most accurate statement.
Final Answer Therefore, the correct answer is:
Any amount of time over an hour and a half would cost $10.
Examples
Imagine you're at an arcade that charges based on time spent playing games online. This problem helps you understand how the cost changes depending on how long you play. Understanding piecewise functions like this can help you budget your time and money effectively, whether it's for gaming, using a co-working space, or any service with tiered pricing.
