The temperature, T, in °C, of a potato put into an oven is given as a function of time, t, in minutes, by T = a(1 - e-kt) + b. (a) Knowing that the temperature of the potato is initially 17°C tells us that OT(17) = 0 O T'(17) = 0 O T'(0) = 17 O T(0) = 17 Knowing that the temperature of the oven is a constant 275°C tells us that Olim T(t) = 275 t→∞ lim T(t) = 00 t18 Olim (t) = 275 a = lim T(t) = 17 t→∞ (b) Use the information in part (a) to find the exact values of a and b. b = (c) Knowing that the temperature of the potato is initially increasing 4°C per minute tells us that O T(0) = 4 OT(4) = 0 O T(1) = 21 OT'(0) = 4 O T'(4) = 0
The temperature, T, in °C, of a potato put into an oven is given as a function of time, t, in minutes, by T = a(1 - e-kt) + b. (a) Knowing that the temperature of the potato is initially 17°C tells us that OT(17) = 0 O T'(17) = 0 O T'(0) = 17 O T(0) = 17 Knowing that the temperature of the oven is a constant 275°C tells us that Olim T(t) = 275 t→∞ lim T(t) = 00 t18 Olim (t) = 275 a = lim T(t) = 17 t→∞ (b) Use the information in part (a) to find the exact values of a and b. b = (c) Knowing that the temperature of the potato is initially increasing 4°C per minute tells us that O T(0) = 4 OT(4) = 0 O T(1) = 21 OT'(0) = 4 O T'(4) = 0
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:The temperature, T, in °C, of a potato put into an oven is given as a function of time, t, in minutes, by T = a(1 - e-kt) + b.
(a) Knowing that the temperature of the potato is initially 17°C tells us that
O T(17) = 0
O T'(17) = 0
O T'(0) = 17
OT(0) = 17
Knowing that the temperature of the oven is a constant 275°C tells us that
Olim (t) = 275
t→∞
lim T(t) = 00
t→∞
O lim T(t) = 275
t → 0
a =
lim T(t) = 17
t→∞o
(b) Use the information in part (a) to find the exact values of a and b.
b =
(c) Knowing that the temperature of the potato is initially increasing 4°C per minute tells us that
OT(0) = 4
O T(4)
O T(1) = 21
O T'(0) = 4
O T'(4) = 0
= 0
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