Answer :
To solve the problem and determine what the temperature of the ice cream will be after 11 hours, we need to first understand the pattern or trend from the data provided. Let's go step-by-step:
Analyze the Provided Data:
We have temperatures recorded at different times during the freezing process:
- At 0 hours: [tex]40^{\circ} F[/tex]
- At 1 hour: [tex]39.2^{\circ} F[/tex]
- At 2 hours: [tex]38.4^{\circ} F[/tex]
- At 3 hours: [tex]37.6^{\circ} F[/tex]
- At 5 hours: [tex]36.2^{\circ} F[/tex]
- At 8 hours: [tex]34^{\circ} F[/tex]
Identify the Pattern:
We observe that the temperature decreases over time. To estimate the temperature at 11 hours, we'll assume a linear trend between the hours and the temperatures.
Calculate the Rate of Decrease:
Let's calculate the average rate of temperature decrease per hour:
- Between 0 and 8 hours, the temperature drop is [tex]40 - 34 = 6^{\circ} F[/tex].
- The time span is 8 hours.
- Therefore, the average rate of decrease is [tex]\frac{6}{8} = 0.75^{\circ} F[/tex] per hour.
Predict the Temperature at 11 Hours:
- From 8 hours to 11 hours, there are 3 hours.
- The estimated decrease over this period is [tex]3 \times 0.75 = 2.25^{\circ} F[/tex].
- Starting from [tex]34^{\circ} F[/tex] at 8 hours, the predicted temperature is:
[tex]34 - 2.25 = 31.75^{\circ} F[/tex].
Rounding to the nearest tenth gives [tex]31.8^{\circ} F[/tex]. However, considering the options given, the closest value is [tex]31.4^{\circ} F[/tex].
Choose the Closest Option:
Based on our calculations, the closest approximation for the temperature after 11 hours is:
B. [tex]31.4^{\circ} F[/tex]
Hence, the correct answer is option B.
