Answer :
Sure, let's break down the problem step-by-step and understand each part.
### Question 19:
You put a yam in the oven. After 45 minutes, you take it out. Let [tex]\( f(t) \)[/tex] be the temperature of the yam [tex]\( t \)[/tex] minutes after you placed it in the oven. In parts a to d, explain the meaning of the statements in everyday language.
#### a. [tex]\( f(0) = 65 \)[/tex]
Explanation:
- [tex]\( f(t) \)[/tex] represents the temperature of the yam at time [tex]\( t \)[/tex].
- [tex]\( f(0) = 65 \)[/tex] means that the temperature of the yam when you first put it in the oven (at [tex]\( t = 0 \)[/tex] minutes) is 65 degrees Fahrenheit.
In everyday language:
- When you first place the yam in the oven, its temperature is 65 degrees Fahrenheit.
#### b. [tex]\( f(5) < f(10) \)[/tex]
Explanation:
- [tex]\( f(5) \)[/tex] is the temperature of the yam at 5 minutes.
- [tex]\( f(10) \)[/tex] is the temperature of the yam at 10 minutes.
- [tex]\( f(5) < f(10) \)[/tex] means the temperature of the yam at 5 minutes is less than its temperature at 10 minutes.
In everyday language:
- After being in the oven for 5 minutes, the yam is cooler than it is at 10 minutes. This indicates the yam is heating up over time in the oven.
#### c. [tex]\( f(40) = f(45) \)[/tex]
Explanation:
- [tex]\( f(40) \)[/tex] is the temperature of the yam at 40 minutes.
- [tex]\( f(45) \)[/tex] is the temperature of the yam at 45 minutes.
- [tex]\( f(40) = f(45) \)[/tex] means the temperature of the yam at 40 minutes is the same as its temperature at 45 minutes.
In everyday language:
- The temperature of the yam doesn't change between 40 minutes and 45 minutes. This might suggest that the yam has reached the oven's maximum temperature, or it is at a steady state.
#### d. [tex]\( f(45) > f(60) \)[/tex]
Explanation:
- [tex]\( f(45) \)[/tex] is the temperature of the yam at 45 minutes.
- [tex]\( f(60) \)[/tex] is the temperature of the yam at 60 minutes.
- [tex]\( f(45) > f(60) \)[/tex] means the temperature of the yam at 45 minutes is higher than its temperature at 60 minutes.
In everyday language:
- After you take the yam out of the oven at 45 minutes, it starts cooling down. The yam's temperature at 60 minutes (15 minutes out of the oven) is lower than it was when you took it out at 45 minutes.
These explanations correspond to the given answers accurately and explain the situation in everyday terms.
### Question 19:
You put a yam in the oven. After 45 minutes, you take it out. Let [tex]\( f(t) \)[/tex] be the temperature of the yam [tex]\( t \)[/tex] minutes after you placed it in the oven. In parts a to d, explain the meaning of the statements in everyday language.
#### a. [tex]\( f(0) = 65 \)[/tex]
Explanation:
- [tex]\( f(t) \)[/tex] represents the temperature of the yam at time [tex]\( t \)[/tex].
- [tex]\( f(0) = 65 \)[/tex] means that the temperature of the yam when you first put it in the oven (at [tex]\( t = 0 \)[/tex] minutes) is 65 degrees Fahrenheit.
In everyday language:
- When you first place the yam in the oven, its temperature is 65 degrees Fahrenheit.
#### b. [tex]\( f(5) < f(10) \)[/tex]
Explanation:
- [tex]\( f(5) \)[/tex] is the temperature of the yam at 5 minutes.
- [tex]\( f(10) \)[/tex] is the temperature of the yam at 10 minutes.
- [tex]\( f(5) < f(10) \)[/tex] means the temperature of the yam at 5 minutes is less than its temperature at 10 minutes.
In everyday language:
- After being in the oven for 5 minutes, the yam is cooler than it is at 10 minutes. This indicates the yam is heating up over time in the oven.
#### c. [tex]\( f(40) = f(45) \)[/tex]
Explanation:
- [tex]\( f(40) \)[/tex] is the temperature of the yam at 40 minutes.
- [tex]\( f(45) \)[/tex] is the temperature of the yam at 45 minutes.
- [tex]\( f(40) = f(45) \)[/tex] means the temperature of the yam at 40 minutes is the same as its temperature at 45 minutes.
In everyday language:
- The temperature of the yam doesn't change between 40 minutes and 45 minutes. This might suggest that the yam has reached the oven's maximum temperature, or it is at a steady state.
#### d. [tex]\( f(45) > f(60) \)[/tex]
Explanation:
- [tex]\( f(45) \)[/tex] is the temperature of the yam at 45 minutes.
- [tex]\( f(60) \)[/tex] is the temperature of the yam at 60 minutes.
- [tex]\( f(45) > f(60) \)[/tex] means the temperature of the yam at 45 minutes is higher than its temperature at 60 minutes.
In everyday language:
- After you take the yam out of the oven at 45 minutes, it starts cooling down. The yam's temperature at 60 minutes (15 minutes out of the oven) is lower than it was when you took it out at 45 minutes.
These explanations correspond to the given answers accurately and explain the situation in everyday terms.
