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Answer :
Sure! Let's go through each part of the question step by step.
Part a: Explain what [tex]\( P(30) = 350 \)[/tex] represents in this context.
In the context of the pumpkin pie recipe, the function [tex]\( P(t) \)[/tex] gives the oven temperature setting in degrees Fahrenheit, [tex]\( t \)[/tex] minutes after the pie is placed in the oven. Therefore, [tex]\( P(30) = 350 \)[/tex] means that after 30 minutes from when the pie was placed in the oven, the oven's temperature setting is at 350°F. This reflects the recipe's instruction to adjust the oven to 350°F after an initial period at 425°F.
Part b: What is the corresponding point on the function [tex]\( B \)[/tex] if [tex]\( P(30) = 350 \)[/tex]?
Diego has discovered that the actual temperature inside the oven is always 25 degrees warmer than the oven's temperature setting. Given that the setting at 30 minutes is 350°F, the real temperature inside the oven will be 25 degrees warmer. Therefore:
If [tex]\( P(30) = 350 \)[/tex], then the actual temperature [tex]\( B(30) \)[/tex] will be:
[tex]\[ B(30) = P(30) + 25 = 350 + 25 = 375 \][/tex]
So, the corresponding point on the function [tex]\( B \)[/tex] is [tex]\( B(30) = 375 \)[/tex].
Part c: Write an expression for [tex]\( B \)[/tex] in terms of [tex]\( P \)[/tex].
Since Diego found that the actual oven temperature is consistently 25 degrees higher than the oven's setting, we can express the actual temperature function [tex]\( B(t) \)[/tex] as:
[tex]\[ B(t) = P(t) + 25 \][/tex]
This formula allows you to calculate the real temperature in Diego's oven based on any oven setting [tex]\( P(t) \)[/tex].
Part a: Explain what [tex]\( P(30) = 350 \)[/tex] represents in this context.
In the context of the pumpkin pie recipe, the function [tex]\( P(t) \)[/tex] gives the oven temperature setting in degrees Fahrenheit, [tex]\( t \)[/tex] minutes after the pie is placed in the oven. Therefore, [tex]\( P(30) = 350 \)[/tex] means that after 30 minutes from when the pie was placed in the oven, the oven's temperature setting is at 350°F. This reflects the recipe's instruction to adjust the oven to 350°F after an initial period at 425°F.
Part b: What is the corresponding point on the function [tex]\( B \)[/tex] if [tex]\( P(30) = 350 \)[/tex]?
Diego has discovered that the actual temperature inside the oven is always 25 degrees warmer than the oven's temperature setting. Given that the setting at 30 minutes is 350°F, the real temperature inside the oven will be 25 degrees warmer. Therefore:
If [tex]\( P(30) = 350 \)[/tex], then the actual temperature [tex]\( B(30) \)[/tex] will be:
[tex]\[ B(30) = P(30) + 25 = 350 + 25 = 375 \][/tex]
So, the corresponding point on the function [tex]\( B \)[/tex] is [tex]\( B(30) = 375 \)[/tex].
Part c: Write an expression for [tex]\( B \)[/tex] in terms of [tex]\( P \)[/tex].
Since Diego found that the actual oven temperature is consistently 25 degrees higher than the oven's setting, we can express the actual temperature function [tex]\( B(t) \)[/tex] as:
[tex]\[ B(t) = P(t) + 25 \][/tex]
This formula allows you to calculate the real temperature in Diego's oven based on any oven setting [tex]\( P(t) \)[/tex].
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