In a northwestern U.S. town, the peak temperature is 96° Fahrenheit in August. After the peak, it drops an average of 4° Fahrenheit per week. The graph below models the number of weeks it would take the temperature to drop below freezing, 32° Fahrenheit.

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Which of the following is the correct interpretation of the solution?
A.
It would take 16 or less weeks to drop below freezing.
B.
It would take less than 16 weeks to drop below freezing.
C.
It would take 16 or more weeks to drop below freezing.
D.
It would take more than 16 weeks to drop below freezing.

1 answer

To analyze the problem, let's determine how long it takes for the temperature to drop from 96° Fahrenheit to below 32° Fahrenheit.

  1. The temperature drops an average of 4° Fahrenheit per week.
  2. The total temperature drop needed to reach below freezing is: \[ 96° - 32° = 64° \text{ Fahrenheit} \]
  3. To find out how many weeks it takes to drop 64° Fahrenheit: \[ \text{Weeks} = \frac{64°}{4°/\text{week}} = 16 \text{ weeks} \]

Since the problem involves dropping below freezing, this implies that it will take exactly 16 weeks to reach 32°, and just a bit longer to drop below it.

Now, interpreting the options:

  • A: It would take 16 or less weeks to drop below freezing. (Incorrect, it takes exactly 16 weeks to reach 32° but not below freezing.)
  • B: It would take less than 16 weeks to drop below freezing. (Incorrect, it takes exactly 16 weeks to reach 32°.)
  • C: It would take 16 or more weeks to drop below freezing. (Correct, it takes 16 weeks to reach 32° and will take more than 16 weeks to go below freezing.)
  • D: It would take more than 16 weeks to drop below freezing. (While this is true, the "16 or more" option is a more comprehensive answer.)

Thus, the correct interpretation of the solution is C. It would take 16 or more weeks to drop below freezing.