The number of problems assigned as homework by a savvy math professor is a function of the length of the class on a particular day, which is either 45 minutes, 90 minutes, or 135 minutes. He first multiplies the number of minutes by 4 and then divides that number by 9 . Finally, he subtracts 12 from that amount. Which of the following functions best represents the number of math problems the professor assigns depending on the length of the class, t, in minutes? Choose 1 answer: (A) f(t)=(4)/(9)t-12 (B) f(t)=(4)/(9)(t-12) (c) f(t)=12-(4)/(9)t (D) f(t)=12+(4)/(9)t

Question

The number of problems assigned as homework by a savvy math professor is a function of the length of the class on a particular day, which is either 45 minutes, 90 minutes, or 135 minutes. He first multiplies the number of minutes by 4 and then divides that number by 9 . Finally, he subtracts 12 from that amount. Which of the following functions best represents the number of math problems the professor assigns depending on the length of the class,  t, in minutes? Choose 1 answer: (A)  f(t)=(4)/(9)t-12 (B)  f(t)=(4)/(9)(t-12) (c)  f(t)=12-(4)/(9)t (D)  f(t)=12+(4)/(9)t

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Problem Understanding: Understand the problem. The professor's method for determining the number of problems is to multiply the class length in minutes by 4, divide by 9, and then subtract 12. We need to translate this process into a function of t, where t represents the class length in minutes.Mathematical Function Translation: Translate the professor's method into a mathematical function. First, he multiplies the number of minutes (t) by 4, which gives us 4t. Then, he divides that number by 9, which can be represented as (4t)/9 or (4/9)t. Finally, he subtracts 12 from that amount, which gives us the function f(t) = (4/9)t - 12.Matching Function with Choices: Match the function with the given choices. The function we derived from the professor's method is f(t) = (4/9)t - 12. Now we need to find which choice matches this function. (A) f(t) = (4/9)t - 12 (B) f(t) = (4/9)(t - 12) (C) f(t) = 12 - (4/9)t (D) f(t) = 12 + (4/9)tChoosing the Correct Function: Choose the correct function. By comparing the function we derived with the choices, we can see that choice (A) f(t) = (4/9)t - 12 is the correct representation of the professor's method for assigning homework problems.

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