What was the average rate of change per minute during the first 30 minutes? (Round your answer to two decimal places.)What was the average rate of change per minute during the second 30 minutes? (Round your answer to two decimal places.)Explain how you got your answer. (Hint: If the potato were left in the oven for a long time, its temperature would match that of the oven.) A potato is placed in a preheated oven to bake. Its temperature P = P(t) is given by the following.P = 400 - 325e-t/50Here P is measured in degrees Fahrenheit and t is the time in minutes since the potato was placed in the oven.(a) Make the graph of P versus t. (Suggestion: In choosing your graphing window, it is reasonable to look at the potato over no more than a 2-hour period. After that, it will surely be burned to a crisp. You may wish to look at a table of values to select span. Select the correct graph.)400-OO300-P 200-400-300P 200-1002020404060t (min)concave down60t (min)8080100(d) Is this graph concave up or concave down?O concave up120120O400300-P 200-O The temperature is not falling as fast at later times as it was at first.The temperature is not rising as fast at later times as it was at first.O The temperature is falling faster at later times than it was at first.100400-Explain what that tells you about how the potato heats up, and relate this to part (c).O The temperature is rising faster at later times than it was at first.300-P 200(b) What was the initial temperature of the potato? (Round your answer to the nearest whole number.)79x °F(c) Did the potato's temperature rise more during the first 30 minutes or the second 30 minutes of baking?first 30 minO second 30 min100-20What was the average rate of change per minute during the first 30 minutes? (Round your answer to two decimal places.)375x deg/min40What was the average rate of change per minute during the second 30 minutes? (Round your answer to two decimal places.)1x deg/min37560t (min)t (min)80100100120120(e) The potato will be done when it reaches a temperature of 270 degrees. Approximate the time when the potato will be done. (Round your answer to the nearest whole number.) (e) The potato will be done when it reaches a temperature of 270 degrees. Approximate the time when the potato will be done. (Round your answer to the nearest whole number.)45✔min(f) What is the temperature of the oven? (Round your answer to the nearest whole number.)400✔ °FExplain how you got your answer. (Hint: If the potato were left in the oven for a long time, its temperature would match that of the oven.)

Given- A potato is placed in a preheated oven to bake. Its temperature P = Pt is given by the…

What was the average rate of change per minute during the first 30 minutes? (Round your answer to two decimal places.) What was the average rate of change per minute during the second 30 minutes? (Round your answer to two decimal places.) Explain how you got your answer. (Hint: If the potato were left in the oven for a long time, its temperature would match that of the oven.)

What was the average rate of change per minute during the first 30 minutes? (Round your answer to two decimal places.) What was the average rate of change per minute during the second 30 minutes? (Round your answer to two decimal places.) Explain how you got your answer. (Hint: If the potato were left in the oven for a long time, its temperature would match that of the oven.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

What was the average rate of change per minute during the first 30 minutes? (Round your answer to two decimal places.)

What was the average rate of change per minute during the second 30 minutes? (Round your answer to two decimal places.)

Explain how you got your answer. (Hint: If the potato were left in the oven for a long time, its temperature would match that of the oven.)

A potato is placed in a preheated oven to bake. Its temperature P = P(t) is given by the following.
P = 400 - 325e-t/50
Here P is measured in degrees Fahrenheit and t is the time in minutes since the potato was placed in the oven.
(a) Make the graph of P versus t. (Suggestion: In choosing your graphing window, it is reasonable to look at the potato over no more than a 2-hour period. After that, it will surely be burned to a crisp. You may wish to look at a table of values to select span. Select the correct graph.)
400-
O
O
300-
P 200-
400-
300
P 200-
100
20
20
40
40
60
t (min)
concave down
60
t (min)
80
80
100
(d) Is this graph concave up or concave down?
O concave up
120
120
O
400
300-
P 200-
O The temperature is not falling as fast at later times as it was at first.
The temperature is not rising as fast at later times as it was at first.
O The temperature is falling faster at later times than it was at first.
100
400-
Explain what that tells you about how the potato heats up, and relate this to part (c).
O The temperature is rising faster at later times than it was at first.
300-
P 200
(b) What was the initial temperature of the potato? (Round your answer to the nearest whole number.)
79
x °F
(c) Did the potato's temperature rise more during the first 30 minutes or the second 30 minutes of baking?
first 30 min
O second 30 min
100-
20
What was the average rate of change per minute during the first 30 minutes? (Round your answer to two decimal places.)
375
x deg/min
40
What was the average rate of change per minute during the second 30 minutes? (Round your answer to two decimal places.)
1x deg/min
375
60
t (min)
t (min)
80
100
100
120
120
(e) The potato will be done when it reaches a temperature of 270 degrees. Approximate the time when the potato will be done. (Round your answer to the nearest whole number.)

(e) The potato will be done when it reaches a temperature of 270 degrees. Approximate the time when the potato will be done. (Round your answer to the nearest whole number.)
45
✔min
(f) What is the temperature of the oven? (Round your answer to the nearest whole number.)
400
✔ °F
Explain how you got your answer. (Hint: If the potato were left in the oven for a long time, its temperature would match that of the oven.)

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