Question

you put a yam in the oven. after 45 minutes, you take it out. let f(t) be the temperature of the yam t minutes after you placed it in the oven. in (a)-(d), explain the meaning of the statement in everyday language. write in full sentences and draw a graph to represent the situation. a. f(0)=65 b. f(5)<f(10) c. f(40)=f(45) d. f(45)>f(60)

Explanation:

a. The temperature of the yam at the moment it is placed in the oven (0 minutes after placement) is 65 degrees.
b. The temperature of the yam 5 minutes after being placed in the oven is lower than its temperature 10 minutes after being placed in the oven, indicating it is heating up over time.
c. The temperature of the yam 40 minutes after being placed in the oven is the same as its temperature 45 minutes after being placed in the oven. This could mean it has reached a steady - state temperature in the oven in that time - interval or the oven temperature is constant in that period.
d. The temperature of the yam 45 minutes after being placed in the oven (when it is taken out) is higher than its temperature 15 minutes later (60 minutes from the start). This implies that after being taken out of the oven, the yam starts to cool down.

To draw the graph:

• On the x - axis, label it as "Time (t in minutes)" with values from 0 to 60.
• On the y - axis, label it as "Temperature of the yam (f(t))".
• For a, mark the point (0, 65).
• For b, show that the function value at t = 5 is lower than at t = 10 as the function is increasing in that interval.
• For c, show a horizontal line segment between t = 40 and t = 45 indicating the constant temperature.
• For d, show that the function value at t = 45 is higher than at t = 60 as the function is decreasing after t = 45.

Answer:

a. The temperature of the yam when first put in the oven is 65 degrees.
b. The yam is hotter 10 minutes after being put in the oven than 5 minutes after being put in the oven.
c. The temperature of the yam is the same 40 minutes and 45 minutes after being put in the oven.
d. The yam is hotter right when it is taken out of the oven (45 minutes) than 15 minutes after it is taken out (60 minutes).